2. unit 2 tvm

Unit No. 2

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“Never spend your money before you have it” Thomas Jefferson

Interest

Motives for Holding Money

Types of Interest

Types of Interest Rates

Investment Evaluation by

TVM

FV of Lump sum (Annual Compounding)

FV of Lump sum (Intra Year Compounding)

Yield Curve

Unit 2 Roadmap

Fixed

Combined

Floating

Simple

Continuous Compound

Discrete Compound

General Formula

Factor Formula

General Formula

Factor Formula

Transaction

Speculative

Precautionary

Finance

Work Book Foundation Level 14 Time Value of Money

Unit 2

TIME VALUE OF MONEY (TVM)

Rupee today is worth more than will tomorrow

Because Inflation (Persistent rise in the general price level over a period of time) and

Opportunity Cost (The cost of next best alternative forgone)

If Cash Flow certain than TVM = Interest Rate

If Cash Flow uncertain than TVM = Interest Rate + Risk Premium

2.1 The Interest Fee paid on borrowed money

Compensation to lender for foregoing other useful investment

Equilibrium price at which demand and supply of fund meet

Formula

I = Interest (The charge for the privilege of borrowing money, typically expressed as an annual percentage rate APR)

RR = Real Rate (An absolutely risk-free investment over a specified period of time)

IF = Inflation Factor (The rate at which the general level of prices for goods and services is rising)

DR = Default Risk (Default risks that companies or individuals will be unable to make the required payments on their

debt obligations)

MR = Maturity Risk (Risk associated with interest rate uncertainty. The longer the time to maturity, the higher the

premium)

2.2 Types of Interest It is cost to borrow money. The rent one pays for the use of money is called the interest.

There are three types of interest

2.2.1 Simple Interest

Interest calculated on principal amount only

Although the interest rate is often specified for a year, it may be specified for a week, a month, or a quarter, etc.

Formula

SIn = Simple Interest for n time period P = Principal Amount

i = Rate of Interest n = Time period

Example 2.1: Mr. Salman has three options for investment. Option first offered by Allied Bank is deposit Rs. 100 in a

five-year certificate of deposit paying 10% simple interest p.a. How much will he have at the end of the fifth year?

I = RR + IF + DR + MR + …………..

SIn = P + (P * i * n)

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Unit 2

Solution

2.2.2 Discrete Compound Interest

Interest on principal as well as on interest is called discrete compound interest or compound interest

Formula

CIn = Compound Interest for n time period P = Principal Amount

i = Rate of Interest n = Time period

Example 2.2: Mr. Salman has second option offered by National Bank is deposit Rs. 100 in a five-year certificate of

deposit paying 10% discrete compound interest. How much will he have at the end of the fifth year? Find out the

difference of interest between compound and simple interest?

Solution

Difference of Interest = Compound interest - Simple Interest

Difference of Interest = 161.05 – 150 = Rs. 11.05

This mean interest on principal is Rs. 50 and interest on interest is Rs. 11.05

2.2.3 Continuous (Exponential) Compound Interest

As the name suggests that it has exponentially increased rate of interest

When interest is compounded "many times", we say that the interest is compounded continuously

Formula

EIn = Continuous interest for n time period P = Principal amount

e = exponent with constant (2. 718) i = Rate of return

n = Number of years

CIn = P (1 + i) n

EIn = P * e i * n

SIn = P + (P * i * n)

SI5 = 100 + (100 * 0.10 * 5)

SI5 = Rs. 150

CIn = P (1 + i) n

CI5 = 100 (1 + 10/100) 5

CI5 = 100 (1.10) 5

CI5 = Rs. 161.05

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Unit 2

Example 2.3: Last option for Mr. Salman which offered by United Bank is deposit Rs. 100 in a five-year certificate of

deposit paying 10% continuous compound interest. How much will he have at the end of the fifth year? Which is best

choice?

Solution

Option No. Type of Interest Bank Future Value

1 Simple Allied Bank Rs. 150

2 Discrete Compound National Bank Rs. 161.05

3 Continuous Compound United Bank 164.86 (Best choice)

If you are depositor select Continuous Compounding Interest assuming same rate for all other alternatives

If you are lender select Simple Interest assuming same rate for all other alternatives

2.3 Types of Interest Rates There are three types of interest are generally used

2.3.1 Fixed Interest Rates

Stated and unchanged rate of interests

2.3.2 Floating / Market Interest Rates

Fluctuating rate of interest based on market conditions

2.3.3 Combined / Dictated Interest Rates

Mix of fixed and floating rate of interests

EIn = P * e i * n

EI5 = 100 * 2.718 0.10 * 5

EI5 = Rs. 164.87

Continuous

Compound

Simple

Interest Rates

Fixed Floating Combined

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Unit 2

2.4 Investment Evaluation by Time Value of Money There are two Time Value of Money techniques are used to evaluate investments

2.4.1 Future Value of Lump sum amount (Annual Compounding)

The value of lump sum amount (one time cash flow) at some future time evaluated at a given interest rate

assuming that compounding take place one time in a year (Annually)

Two methods for calculation

Or

Or

FVn = Future value of n years PV = Present value i = Interest rate or Compound rate

n = Number of years FVIF = Future Value Interest Factor

FV of Lump sum (Annual Compounding)

General Formula Factor Formula

Floating Rate Constant Rate

FVn = PV (1 + i) * (1 + i) * (1 + i) *……..……* (1 + i) for n times General Formula

Floating Rate

FVn = PV (1 + i) n General Formula

Constant Rate

FVn = PV (FVIF i%, n) Factor Formula

Constant Rate

Lump sum Annuity Lump sum Annuity

Time Value of Money

Future Value / Compounding Present Value / Discounting

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Unit 2

Example 2.4: Ms. Nosheen puts Rs. 10,000 in a savings account today, that pays 5% compounded annually. How much

will she have in her account after ten years; by above mentioned three equations?

General Formula Floating Rate

General Formula Constant Rate

Factor Formula

Example 2.5: Find the value of Rs. 10,000 today at the end of 10 periods at 5% per period by using scientific calculator

and by Excel sheet?

Scientific Calculator:

1. Enter 10,000 (1 + 0.05)

2. Press xn

3. Enter the exponent 10

4. Enter =

5. Answer Rs. 16,288.95

KEY RELATIONHSIP

FVn = PV (1 + i) n

FVn = PV (1+i) * (1+i) * (1+i) * (1+i) * (1+i) * (1+i) * (1+i) * (1+i) * (1+i) *(1+i)

FV10 = 10,000 (1.05) * (1.05) * (1.05) * (1.05) * (1.05) * (1.05) * (1.05) * (1.05) * (1.05) * (1.05)

FV10 = 10,000 * 1.6289

FV10 = Rs. 16,289

FVn = PV (1 + i) n

FV10 = 10,000 (1 + 0.05)10

FV10 = 10,000 * 1.62889

FV10 = Rs. 16,289

FVn = PV (FVIF i%, n)

FVn = 10,000 (FVIF 5%, 10)

FVn = 10,000 (1.6289)

FV10 = Rs. 16,289

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Unit 2

Spreadsheet:

2.4.2 Future Value of Lump sum amount (Intra Year Compounding)

The value of lump sum amount (one time cash flow) at some future time evaluated at a given interest rate

assuming that compounding takes place more than one time in a year (Intra Year)

Interest rate reduced while periods of time increase by frequency of compounding (m) i.e. i/m and n*m

Two methods for calculation

Or

FVn = Future value of n years PV = Present value

i = Interest rate or Compound rate m = Frequency of compounding

n = Number of years FVIF = Future Value Interest Factor

Example 2.6: Mr. Naveed purchased a 3-year, 6-percent savings certificate for Rs. 25,000. If interest is compounded

semi-annually, what will be the value of the certificate when it matures by above mentioned two equations?

General Formula

FVn = PV (1 + i / m) n * m

FV3 = 25,000 (1 + 0.06 / 2) 3 * 2

FV3 = 25,000 (1.1941)

FV3 = Rs. 29,852.5

FV of Lump sum (Intra Year Compounding)

General Formula Factor Formula

FVn = PV (mn

miFVIF

*,% ) Factor Formula

FVn = PV (1 + i / m) n * m General Formula

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Unit 2

Factor Formula

2.5 Yield Curve The yield curve is the relation between the interest rate and the time to maturity of the debt

More formal mathematical descriptions of this relation are often called the term structure of interest rates

2.6 Motives for holding money Usually there are three defined motives of holding money

2.6.1 Transactions Motives

Need money to be able to spend it, and so hold balances of money appropriate for that

Like the amount of money that you have in your pocket

2.6.2 Precautionary Motives

Unexpected bills or contingencies may mean that we need to hold a

little extra money in case

Like the money we hold in bank current accounts

2.6.2 Speculative Motives

o The speculative motives for money is the amount held for the potential

purchase of assets

o There are of course a number of different ways, which can briefly split it into interest bearing assets or non-

interest bearing assets

o The interest rate and the ease of access may be two important factors in determining this decision

FVn = PV (mn

miFVIF

*,% )

FV3 = 25,000 (2*3,

26FVIF )

FV3 = 25,000 (1.1941)

FV3 = Rs. 29,852.5

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Unit 2

END-OF-UNIT ASSIGNMENT

(PROBLEMS & MULTIPLE CHOICE QUESTIONS)

Problem 2.1: Calculate simple interest and compound interest assuming that principal amount is Rs. 10,000; interest rate

is 9% for three years. What is the amount difference between compound and simple interest?

Year

Simple Interest Calculation

Compound Interest Calculation

Simple Interest

Calculation

Simple

Interest

Accumulated

Year-end

Balance

Compound

Interest

Calculation

Compound

Interest

Accumulated

Year-end

Balance

Yr 1 Rs. 10,000 * 9% Rs. 900 Rs. 10,900 Rs. 10,000 * 9% Rs. 900 Rs. 10,900

Yr 2 10,000 * 9% 900 11,800 10,900 * 9% 981.00 Rs. 11,881.00

Yr 3 10,000 * 9% 900 12,700 11,880.10 * 9% 1069.29 Rs. 12,950.29

Total Rs. 2,700 Rs. 2,950.29

Difference = 2,950.29 - 2,700 = Rs. 250.29

Problem 2.2: You are scheduled to receive Rs. 13,000 in two years. When you receive it, you will invest it for six more

years at 8 percent per year. How much will you have in eight years?

Solution: 13,000 (1 + 0.08) 6

Answer: Rs. 20,629.37

Problem 2.3: You have Rs. 9,000 to deposit. ABC Bank offers 12 percent per year compounded monthly, while King

Bank offers 12 percent but will only compound annually. How much will your investment be worth in 10 years at each

bank?

Solution: ABC Bank 9,000 (1 + 0.12/12) 10 * 12 Answer: Rs. 29,703.48

King Bank 9,000 (1 + 0.12) 10 Answer: Rs. 27,952.63

Variance Rs. 1,750.85

Problem 2.4: You invest Rs. 10,000. During the first year the investment earned 20% for the year. During the second

year, you earned only 4% for that year. How much is your original deposit worth at the end of the two years?

Solution: FV =10,000 (1.20) (1.04)

Answer: Rs. 12,480

Problem 2.5: Ali deposited Rs. 2,500 in an account that pays 6% simple interest. How much money will he have at the

end of 3 years?

Solution: 2,500 + (2,500 * 0.06 * 3)

Answer: Rs. 2,950

Finance


Unit 2

Problem 2.6: What is the future value of Rs. 26 invested for 32 years at an average rate of return of 7%?

Solution: FV = 26 (1.07) 32

Answer: Rs. 226.60

Problem 2.7: If interest is compounded quarterly, how much will you have in a bank account?

(a) If you deposit today Rs. 8,000 at the end of 3 months, if the bank pays 5.0% APR?

Solution: 8,000 (1 + 0.05 / 4)

Answer: Rs. 8,100

(b) If you deposit today Rs. 10,000 at the end of 6 months, if the bank pays 9.0% APR?

Solution: 10,000 (1 + 0.09 / 4) 2

Answer: Rs. 10,455.06

(c) If you deposit today Rs. 80,000 at the end of 12 months, if the bank pays 8.0% APR?

Solution: 80,000 (1 + 0.08 / 4) 1 * 4

Answer: Rs. 86,594.57

(d) If you deposit today Rs. 5,000 at the end of 24 months, if the bank pays 5.0% APR?

Solution: 5,000 (1 + 0.05 / 4) 2 * 4

Answer: Rs. 5,522.43

Problem 2.8: Find the future value of Rs. 100,000 for 15 years. The current five-year rate is 6%. Rates for the second

and third five-year periods and expected to be 6.5% and 7.5%, respectively.

Solution: FV = 100,000 (1.06)5(1.065)5(1.075)5

FV = 100,000 (1.3382) (1.37009) (1.43563)

FV = 100,000 (2.6322)

Answer: Rs. 263,220

Problem 2.9: The Green Corporation needs Rs. 50 million to repay a loan which is due at the end of seven years. If

Green makes the following sinking fund payments, will there be sufficient funds available to repay the loan on schedule?

Sinking fund contributions

Amount funded Date invested Rate earned

Rs. 12 million today 11%

10 million in two years 10%

8 million in four years 9%

Solution: FV of the Rs. 12 million = 12(1.11)7 = Rs. 24.9139

FV of the Rs. 10 million = 10 (1.1)5 = Rs. 16.1051

FV of the Rs. 8 million = 8(1.09)3 = Rs. 10.3602

Answer: Rs. 51.382 Million

Finance


Unit 2

Problem 2.10: If farm land is currently worth Rs. 1,750 per acre and is expected to increase in value at a rate of 5

percent annually, what will it be worth in 5 years? In 10 years? In 20 years by factor formula and table?

Solution: 5 years: Rs. 1,750 * 1.2763 = Answer: Rs. 2,233.53

10 years: Rs. 1,750 * 1.6289 = Answer: Rs. 2,850.58

20 years: Rs. 1,750 * 2.6533 = Answer: Rs. 4,643.28

Problem 2.11: A Visa credit card company charges a 1.5% simple interest charge each month on the unpaid balance. If

Miss Sehrish owes Rs. 2,350 and has not paid her bill for three months, how much does she owe?

Solution: 2,350 + (2,350 * 0.015 * 3)

2,350 + 105.75


Problem 2.12: If Rs. 3,500 is invested at 9% compounded continuously, what will the future value be in four years?

Solution: 3,500 e 0.09 * 4


Problem 2.13: What is the future value of Rs. 20,000 that grows at an annual interest rate of 12% per year for two years?

Solution: 20,000 (1 + 0.12) 2

Answer: Rs. 25,088

Problem 2.14: What is the future value of Rs. 25,000 which grows at an annual interest rate of 11% per year for five

years with compounding takes place semi-annually?

Solution: 25,000 (1 + 0.11/2) 5*2

Answer: Rs. 42,703.61

Problem 2.15: What is the future value of Rs. 7,000 which grows at a nominal annual interest rate of 8% per year,

compounded monthly, for four years?

Solution: 7,000 (1+ 0.08/12) 4*12


Problem 2.16: Suppose you make an investment of Rs. 1,000. This first year the investment returns 12%, the second

year it returns 6%, and the third year in returns 8%. How much would this investment be worth?

Solution: 1,000 (1.12) (1.06) (1.08)


Problem 2.17: If you put Rs. 100 in the market today at 10%, how much would you end up with in 20 years?

Solution: 100 (1+ 0.10) 20

Answer: Rs. 672.75

Problem 2.18: You apply for a loan of Rs. 5,000 from the bank. Interest will be calculated at a rate of 8.9% compounded

monthly and the loan must be repaid in full within 6 years. What is the total amount you will end up paying back?

Solution: 5,000 (1 + 0.089/12) 6*12


Finance


Unit 2

Problem 2.19: Mr. Ali had opened a savings account on 31st December, 2008 with Rs. 100,000. What will be his account

balance in 31st December, 2012 when compound interest rate is 5 percent per annum?

Date Description Balance (Rs.)

31st, December 2008 Opening an account Rs. 100,000

31st, December 2009 100,000 * 0.05 = Rs. 5,000 Rs. 105,000

31st, December 2010 105,000 * 0.05 = Rs. 5,250 Rs. 110,250

31st, December 2011 110,250 * 0.05 = Rs. 5,512.50 Rs. 115,762.50

31st, December 2012 115,762.50 * 0.05 = Rs. 5,788.13 Rs. 121,550.63

Problem 2.20: Rs. 400 is invested over a period of 20 years at the following nominal rates of interest:

Years 1-5: 3% per annum compound half yearly

Years 6-10: 5% per annum compound quarterly

Years 11-20: 4% per annum compound yearly

Calculate the total accumulation after 20 years

Solution: Years 1-5: 3% per annum compound half yearly 400 (1 + 0.03/2) 5*2 = Rs. 464.22

Years 6-10: 5% per annum compound quarterly 464.22 (1 + 0.05/4) 5*4 = Rs. 595.15

Years 11-20: 4% per annum compound yearly 595.15 (1 + 0.04) 10 = Rs. 880.97

Answer: Rs. 880.97

Problem 2.21: You decide to invest Rs. 300 for 2 years in securities that earns 6.2% simple interest

(a) How much interest will this investment earn?

Solution: (300 * 0.062 * 2)

Answer: Rs. 37.2

(b) How much money will you have in total at the end of the term?

Solution: 300 + (300 * 0.062 *2)

Answer: Rs. 337.2

Problem 2.22: Find the value of Rs. 80,000 for 10 years by factor formula and table. The investment earns 8 percent per

annum?

Solution: FV10 = 80,000 (FVIF 8%, 10)

FV10 = 80,000 (2.1589)

Answer: Rs. 172,712

Problem 2.23: Find the value of Rs. 11,500 compounding quarterly by using continuous compounding method when rate

of interest is 5% and for 3 years?

Solution: FV3 = 11,500 * 2.718 (0.05 / 4) * (3 * 4)

Answer: Rs. 13,361.094

Finance


Unit 2

Problem 2.24: Which loan should you accept (assuming you want to pay as little interest as possible)? Show all your

work.

Option A:

Rs. 6,000 at an interest rate of 12% compounded monthly for 6 years

Solution: 6,000 (1 + 0.12/12) 6*12

Answer: Rs. 12,282.60

Option B:

Rs. 6,000 at an interest rate of 9.8% compounded weekly for 6 years

Solution: 6,000 (1 + 0.098/52) 6*52

Answer: Rs. 10,796.33

Option C:

Rs. 6,000 at a simple interest rate of 13.4% for 6 years

Solution: 6,000 + (6,000 * 0.134 * 6)

Answer: Rs. 10,824

Accept B

Problem 2.25: For each of the following, compute the future value by factor formula?

Present Value Years Interest Rate Factor Future Value

Rs. 3,150 3 16% 1.5609 Rs. 4,916.84

Rs. 7,810 10 6 % 1.7908 Rs. 13,986.15

Rs. 89,305 17 12 % 6.8660 Rs. 613,168.13

Rs. 227,382 22 5 % 2.9253 Rs. 665,160.56

Problem 2.26: Find the value of Rs. 200 by factor formula and table for 120 years. The investment earns 7 % per year.

Solution: FV120 = 2,000 (FVIF 7%, 40) * (FVIF 7%, 40) * (FVIF 7%, 40)

FV120 = 2,000 (14.974) * (14.974) * (14.974)

Answer: Rs. 671,496.080

Problem 2.27: Compute the future value of Rs. 5,000 compounded annually for

a. 10 years at five percent

Solution: 5,000 (1 + 0.05) 10


b. 10 years at seven percent

Solution: 5,000 (1 + 0.07) 10


c. 20 years at five percent

Solution: 5,000 (1 + 0.05) 20

Answer: Rs. 13,266.49

Finance


Unit 2

Problem 2.28: Compute the future value of Rs. 1,000 continuously compounded for

a. Five years at a stated annual interest rate of 12 percent

Solution: 1,000 e 0.12 * 5


b. Three years at a stated annual interest rate of 10 percent

Solution: 1,000 e 0.10 * 3


c. 10 years at a stated annual interest rate of five percent compound semi-annually

Solution: 1,000 e (0.05/2) * (10*2)


Problem 2.29: Choose the investment that will earn you the most money at the end of 10 years?

Option A:

Invest Rs. 7,500 at 8.3% simple interest

Solution: 7,500 (7,500 * 0.083 * 10)

Answer: Rs. 13,725

Option B:

Invest Rs. 7500 at 6.2% interest, compounded quarterly

Solution: 7,500 (1 + 0.062/4) 10*4

Answer: Rs. 13,875.81

Option C:

Invest Rs.7500 at 5.3% interest, compounded daily

Solution: 7,500 (1 + 0.053/365) 10*365

Answer: Rs. 12,741.50

Option D:

Invest Rs. 7500 at 6.0% interest, compounded monthly

Solution: 7,500 (1 + 0.06/12) 10*12

Answer: Rs. 13,645.48

Accept B

Problem 2.30: Find the future value of Rs. 200 after 10 years, compounded at an annual rate of 8 percent by using both

general and factor formula?

Solution: FV10 = 200 (1 + 0.8) 10

Answer: Rs. 431.8

FV10 = 200 (FVIF 8%, 10)

FV10 = 200 (2.159)

Answer: Rs. 431.8

Finance


Unit 2

Problem 2.31: Calculate the value of Rs. 25,000 earning 12 % interest per year for three years, if compounding takes

place monthly. Solve by factor formula and table?

Solution: FV3 = 25,000 * (FVIF 0.12 / 12, 3 * 12)

FV3 = 25,000 * (1.4308)

Answer: Rs. 35,770

Problem 2.32: What if Rs. 700 compounded (a) Semi-annually, (b) Quarterly, (c) Monthly, (d) Weekly and (e) Daily at

an interest rate of 12 % for 5 years?

Solution: FV5 = 700 (1 + 0.12 / 2) 5 * 2


FV5 = 700 (1 + 0.12 / 4) 5 * 4


FV5 = 700 (1 + 0.12 / 12) 5 * 12


FV5 = 700 (1 + 0.12 / 52) 5 * 52

Answer: Rs. 1,274.602

FV5 = 700 (1 + 0.12 / 365) 5 * 365


Problem 2.33: Find the future value of Rs. 1,000 compounded continuously at an annual rate of 6% for 3 years?

Solution: FV3 = 1,000 * 2.718 0.06 * 3


Problem 2.34: First City Bank pays 7% p.a. interest compounded annually on its savings account balances, whereas

Second City Bank pays 7% p.a. interest compounded quarterly. If you made a Rs. 6,000 deposit in each bank; how much

more money would you earn from your Second City Bank account at the end of 8 years?

Solution: First City Bank FV8 = 6,000 (1 + 0.07) 8

Answer: Rs. 10,309.12

Second City Bank FV8 = 6,000 (1 + 0.07 / 4) 8 * 4

Answer: Rs. 10,453.28

Variance 144.16

Problem 2.35: An investor has the possibility to deposit Rs. 500 in one of two potential bank accounts for six years.

Account A offers an interest rate of 5% p.a. compounded semi-annually while Account B offers an interest rate of 4.9%

p.a. compounded quarterly. Which will yield the highest future value?

Solution: Account A 500 (1 + 0.05/2) 6 * 2 Answer: Rs. 672.44

Account B 500 (1 + 0.049/4) 6 * 4 Answer: Rs. 669.70

Accept A

Finance


Unit 2

Problem 2.36: For each of the following, compute the future value?

Present value Years Interest rate Future value

2,250 30 12% 67,409.82

9,310 16 9 36,963.55

76,355 3 19 128,670.32

183,796 7 5 258,619.42

Problem 2.37: If interest is compounded monthly, how much will you have in a bank account?

A. If you deposit Rs. 8,000 today, what will be its worth at the end of 3 months, if the bank pays 5.0% APR?

Solution: 8,000 (1 + 0.05/12) 3


B. If you deposit today Rs. 10,000 at the end of 6 months, if the bank pays 9.0% APR?

Solution: 10,000 (1 + 0.09/12) 6

Answer: Rs. 10,458.52

C. If you deposit today Rs. 80,000 at the end of 12 months, if the bank pays 8.0% APR?

Solution: 80,000 (1 + 0.08/12) 12

Answer: Rs. 86,639.96

D. If you deposit today Rs. 5,000 at the end of 24 months, if the bank pays 5.0% APR?

Solution: 5,000 (1 + 0.05/12) 24


Problem 2.38: An art collector has the opportunity to invest in paintings; the investment requires an outlay of Rs. 2 million.

He is certain that he will be able to sell the paintings for Rs. 2.18 million in one year. He also has the opportunity to invest in

certificates of deposit (CDs) which pay 10% per year. Is the investment in the paintings a good investment?

Solution: 2 (1 + 0.10)

Answer: Rs. 2.2 million (Investment in CDs)

Problem 2.39: If you deposit Rs. 45,000 into an account earning 4% interest compounded quarterly, how much would

you have in 5 years?

Solution: 45,000 (1 + 0.04/4) 5*4

Answer: Rs. 54,908.55

Problem 2.40: If you invest Rs. 2,000 (lump sum) in a retirement account, how much will you have in 40 years at 12

percent?

Solution: 2,000 (1 + 0.12) 40

Answer: Rs. 186,101.94

Finance


Unit 2

Problem 2.41: For each of the following, compute the future value if compound rate is 14 percent?

Cash flows 1 2 3 4 5 Total

W 100 200 300 400 500 1,500

X 600 ----- 400 200 300 1,500

Y ----- ----- 1,200 ---- 300 1,500

Z 500 ----- 400 600 ---- 1,500

Solution: (Round all figure to two decimal places)

Cash flows 1 2 3 4 5 Total

W 168.90 296.31 389.88 456 500 1,811.09

X 1,013.38 ---- 519.84 228 300 2,061.22

Y ---- ---- 1,559.52 ---- 300 1,859.52

Z 844.48 ---- 519.84 684 ---- 2,048.32

Problem 2.42: How much will you pay for a Rs. 200,000 automobile after 10 years if the inflation rate is 20%?

Solution: FV10 = 200,000 * (1 + 0.20) 10

Answer: Rs. 1,238,347.28

Finance


Unit 2

MULTIPLE CHOICE QUESTIONS (MCQS)

1. Interest paid (earned) on only the original principal borrowed (lent) is often referred to as ______________?

(a) Compound interest (b) Future value

(c) Present value (d) Simple interest

2. How much will Rs. 10,000 grow into in 5 years if you earn 10%?

(a) Rs. 13,102 (b) Rs. 16,105 (c) Rs. 16,289 (d) None

3. With continuous compounding at 10% for 30 years, the future value of an investment of Rs. 2,000 is closest to?

(a) Rs. 40,171 (b) Rs. 44,898 (c) Rs. 164,500 (d) None of Above

4. (1 + i)n

(a) PVIF (b) FVIF (c) FVIFA (d) PVIFA

5. As a borrower, you should prefer the bank that ____________________ compound per year?

(a) Less times (b) More times (c) Interest (d) None of the above

6. You deposit Rs. 45,000 into an account at 4% interest compounded quarterly, how much would you have in 5 years?

(a) Rs. 57,908 (b) Rs. 50,602 (c) Rs. 55, 687 (d) Rs. 54,909

7. The Future Value (FV) of Rs. 1,000 in 5 years at 5% interest rate will be?

(a) Rs. 1,000.00 (b) Rs. 1,276.28 (c) Rs. 999.99 (d) Rs. 1,500.52

8. Interest paid (earned) on both the original principal borrowed (lent) and previous interest allowed (earned) is often

referred to as __________?

(a) Compound interest (b) Double interest (c) Simple interest (d) Present value

9. What is the future value of a Rs. 10,000 college tuition fund if the nominal rate of interest is 12 percent compounded

monthly for five years?

(a) Rs. 17,623 (b) Rs. 18,167 (c) Rs. 18,105 (d) Rs. 19,133

10. The value of money to be received in the future is _______the value of the same amount of money in hand today?

(a) Higher than (b) Lower than (c) The same as (d) None of the above

11. Interest has 3 types?

(a) Fixed rate, current rate, market rate (b) Market rate, combination rate, fixed rate

(c) Fixed rate, floating rate, current rate (d) Fixed rate, floating rate, combination rate

12. With continuous compounding at 8 percent for 20 years, what is the approximate future value of a Rs. 20,000 initial

investment?

(a) Rs. 52,000 (b) Rs. 93,219 (c) Rs. 99,061 (d) Rs. 915,240

13. The concept of compound interest refers to?

(a) The process of gradually retiring a debt through periodic payments of principal and interest

(b) The process of servicing a debt with regular interest payments, followed lump sum payment of principal and

interest at the end of the loan term

(c) The process of converting future lump sums and annuities into present values at a stated interest rate

(d) The process of earning interest on an original amount, plus interest on interest previously earned

Finance


Unit 2

14. If compounding more times outcome will be greater value, it is choice of?

(a) Borrower (b) Lender (c) Liabilities holder (d) None

15. If bank giving 12% interest rate per year, then per month it will be?

(a) 1% (b) 12% (c) 5% (d) 6%

16. Which of the following expresses 6.5%?

(a) 0.0065 (b) 6.50 (c) 0.650 (d) 0.0650

17. You invest Rs. 500,000 today at the rate of 8% per year. After 6 years from today you withdraw Rs. 300,000. After

10 years from today you receive the remaining owed. How much will you receive after 10 years from today?

(a) Rs. 591,289 (b) Rs. 602,437 (c) Rs. 671,316 (d) None

18. You invest Rs. 300,000 today at the rate of 10% per year (for the entire length of this investment of Rs. 300,000

from today to year 8). After 5 years from today you invest Rs. 200,000 more at the rate of 12% per year (for the 3

years of this investment of Rs. 200,000 from years 5 to 8). After 8 years from today all your investments are returned

to you. How much will you receive after 8 years from today?

(a) Rs. 901,055 (b) Rs. 924,063 (c) Rs. 947,853 (d) Rs. 969,810

19. You just purchased a piece of land for Rs. 10,000. If you expect a 12% annual rate of return on your investment,

how much will you sell the land for in 10 years?

(a) Rs. 25,000 (b) Rs. 38,720 (c) Rs. 31,058 (d) Rs. 34,310

20. The Time value of money must be considered in total outlay decision because?

(a) Cash inflows and out flows occur at different point (b) Inflation greatly reduce the outflows

(c) A dollar received in future is more value able than a dollar today

(d) Cash flows are not known with certainty

21. Money has time value because?

(a) Individuals prefer future consumption to present consumption

(b) Money today is worth more than money tomorrow in terms of purchasing power

(c) There is a possibility of earning risk free return on money invested today (d) B and C above

22. Given an investment of Rs. 10,000 to be invested for one year?

(a) It is better to invest in a scheme that pays 10% simple interest

(b) It is better to invest in a scheme that pays 10% annual compound interest

(c) Both (a) and (b) provide the same return (d) Don’t invest

23. You invest Rs. 100,000 today at the rate of 8% per year. After 5 years you deposit Rs. 150,000 more. After 7 years

all your investments are returned to you. How much will you receive after 7 years?

(a) Rs. 346,342 (b) Rs. 250,000 (c) Rs. 397,348 (d) Rs. 451,259

24. The real rate of interest reflects compensation for?

(a) Present value (b) Future value (c) Time value of money (d) None of above

25. With continuous compounding at 8 percent for 20 years, what is the approximate future value of a Rs. 20,000 initial

investment?

(a) Rs. 52,000 (b) Rs. 93,219 (c) Rs. 99,061 (d) Rs. 915,240

Finance


Unit 2

26. Which of the following formulas is the correct way to express a future value two years into the future based on a present

value and an interest rate? FV2 =

(a) PV (1 + i) + PV (1 + i) (b) PV (1 +i) (1 + i)

(c) PV (1 + i) 2 (d) B and C

27. The basic rule of the time value of money is

(a) Investments will always be worth more tomorrow than they are today

(b) Its always wiser to save a dollar for tomorrow than to spend it today

(c) A dollar in hand today is worth more than a dollar promised at some time in the future

(d) All of the above express an aspect of the basic rule of time value of money

28. You invest Rs. 100,000 at the rate of 8% per year for 5 years. How much will you receive after 5 years?

(a) Rs. 146,933 (b) Rs. 147,249 (c) Rs. 148,381 (d) Rs. 141,084

29. You invest Rs. 18,000,000 today for 6 years time and the rate of return is 10%. How much do you get in 6 years?

(a) Rs. 29,989,188 (b) Rs. 30,435,151 (c) Rs. 30,423,147 (d) Rs. 31,888,098

30. You invest Rs. 10,000 over 12 years at 5%. What is the amount you receive at the end?

(a) Rs. 17,959 (b) Rs. 18,153 (c) Rs. 18,299 (d) Rs. 18,977

31. A decrease in the demand for loanable funds, holding supply constant, will cause interest rates to?

(a) Increase (b) Decrease (c) Stay the same (d) Not enough information to tell

32. Find the compound amount for the deposit, Rs. 1,900 at 10% compounded quarterly for 4 years?

(a) 2,097.24 (b) 2,781.79 (c) 2,660.00 (d) 2,820.56

33. In which case will an investor receive the most interest?

(a) 10%, compounded monthly (b) 10%, compounded annually

(c) 10%, compounded daily (d) 10%, compounded continuously

34. Treasury bills are?

(a) Issued on a premium basis and pay a fixed annual interest rate

(b) Issued on a discount basis and mature at par (c) Issued on a premium basis and mature at par

(d) Issued on a discount basis and pay a fixed annual interest rate

35. Nominal Interest Rate is also known as?

(a) Annual percentage rate (b) Effective interest Rate

(c) Periodic interest rate (d) Coupon rate

36. How much will accumulate in an account with an initial deposit of Rs. 100, and which earns 10% interest

compounded quarterly for three years?

(a) Rs. 107.69 (b) Rs. 133.10 (c) Rs. 134.49 (d) Rs. 313.84

37. The nominal interest rate can be expressed as?

(a) i = MR + IF + DR + MRP (b) i = RR + IF + GRP + MR

(c) i = RR + IF + DRP + TRP (d) i = RR + IP + DR + MR

38. What is the value of Rs. 750 invested at 7.5% compounded quarterly for 4.5 years (round to nearest Rs. 1)?

(a) Rs. 1,048 (b) Rs. 1,010 (c) Rs. 1,038 (d) Rs. 808

Finance


Unit 2

39. With discrete compounding at 8 percent for 20 years, what is the approximate future value of a Rs. 20,000 initial

investment?

(a) Rs. 52, 000 (b) Rs. 93, 219 (c) Rs. 99, 061 (d) Rs. 915, 240

40. If you place Rs. 50 in a savings account with an interest rate of 7% compounded weekly, what will the investment be

worth at the end of five years (round to nearest dollar)?

(a) Rs. 72 (b) Rs. 70 (c) Rs. 71 (d) Rs. 57

41. If you put Rs. 600 in a savings account that yields an 8% rate of interest compounded weekly, what will the

investment be worth in 37 weeks (round to the nearest rupee)?

(a) Rs. 648 (b) Rs. 635 (c) Rs. 634 (d) Rs. 645

42. If Rs. 1,000 were invested now at a 12% interest rate compounded annually, what would be the value of the

investment in two years?

(a) Rs. 1,188 (b) Rs. 1,210 (c) Rs. 1,254 (d) Rs. 1,160

43. If you put Rs. 900 in a savings account that yields 10% compounded semi-annually, how much money will you have

in the account in three years (round to nearest rupee)?

(a) Rs. 1,340 (b) Rs. 1,170 (c) Rs. 1,227 (d) Rs. 1,206

44. Rs. 20,625 at 12% compounded continuously for 5 years, find the compound interest earned by the deposit (Round

to the nearest paisa)?

(a) Rs. 37,581.20 (b) Rs. 37,577.49 (c) Rs. 13,377.58 (d) Rs. 14,353.97

45. Rs. 5,000 at 7% compounded semiannually for 8 years, find the compound amount for the deposit (Round to the

nearest paisa)?

(a) Rs. 7,800.00 (b) Rs. 6,584.05 (c) Rs. 8,669.93 (d) Rs. 8,590.93

46. Assume that you purchase a 6-year, 8 percent savings certificate for Rs. 1,000. If interest is compounded annually,

what will be the value of the certificate when it matures?

(a) Rs. 630.17 (b) Rs. 1,469.33 (c) Rs. 1,677.10 (d) Rs. 1,586.90

47. Rs. 1,000 invested today at 6% interest would be worth ________________ one year from now?

(a) Rs. 1,600 (b) Rs. 1,060 (c) Rs. 1,160 (d) Rs. 1,006

48. A decrease in the supply for loanable funds, holding demand constant, will cause interest rates to?


49. The value of money results from?

(a) Its backing (b) Rates set by the State Bank (c) Its purchasing power (d) None of the above

50. The basic price that equates the demand for and supply of loanable funds in the financial markets is the _______?

(a) Interest rate (b) yield curve (c) Term structure (d) Cash price

51. If the interest rate is greater than 0%, then a dollar today is worth?

(a) Less than a dollar tomorrow (b) The same as a dollar tomorrow

(c) More than a dollar tomorrow (d) There is not sufficient information to tell

52. In an inflationary period, interest rates have a tendency to?

(a) Fall (b) Rise (c) Stay the same (d) Act erratically

Finance


Unit 2

53. The liquidity preference theory holds that interest rates are determined by the?

(a) Supply of and demand for money (b) Supply of and demand for loanable funds

(c) “Flow” of funds over time (d) “Flow” of bank credit over time

54. The basic motives for holding money rather than investments are?

(a) Transactions motive and the precautionary motive (b) Transactions motive and liquidity preference motive

(c) Transactions motive, the precautionary motive, and the speculative motive

(d) Transactions motive, the precautionary motive, and the liquidity preference motive

55. As the economy begins moving out of a recessionary period, the yield curve is generally?

(a) Upward sloping (b) Flattened out (c) Downward sloping (d) Discontinuous

56. An unexpected increase in inflation should?

(a) Increase the demand for loanable funds (b) Decrease the interest rate on loans

(c) Increase the interest rate on loans (d) None of the above

57. An increase in the supply for loanable funds, holding demand constant, will cause interest rates to?

(a) Decrease (b) Increase (c) Stay the same (d) Not enough information to tell

58. If you expect the inflation premium to be 2%, the default risk premium to be 1% and the real interest rate to be 4%,

what interest would you expect to observe in the marketplace under the simplest form of market interest rates?

(a) 4% (b) 7% (c) 2% (d) 1%

59. Which of the following factors directly impact the level of interest rates?

(a) Risk (b) Marketability (c) Maturity (d) All of the above

60. An increase in the demand for loanable funds, holding supply constant, will cause interest rates to?


61. If the interest rate is less than 0%, then a dollar today is worth?

(a) More than a dollar tomorrow (b) The same as a dollar tomorrow

(c) Less than a dollar tomorrow (d) There is not sufficient information to tell

62. Assume that these current yields exist: long-term government securities yield 9 percent, five-year Treasury securities

yield 8.5 percent, and one-year Treasury bills yield 8 percent. What type of yield curve is depicted?

(a) Downward sloping (b) Flat or level (c) Upward sloping (d) U shaped

63. The future value of Rs. 100 received today and deposited at 6 percent for four years is?

(a) Rs. 126 (b) Rs. 79 (c) Rs. 124 (d) Rs. 116

64. If the nominal interest rate is 8% and the risk-free rate is 3%, the expected inflation rate?

(a) 3% (b) 5% (c) 11% (d) Cannot be determined without additional information

65. Which of the following is not true of Treasury bills?

(a) Long-lived (b) Sold at a discount (c) Mature at par (d) All the above are false

66. The future value of Rs. 200 received today and deposited at 8 percent for three years is?

(a) Rs. 248 (b) Rs. 252 (c) Rs. 158 (d) 200

Finance


Unit 2

67. Which of the following is not a determinant of market interest rates?

(a) The inflation premium (b) The maturity risk premium

(c) The volatility risk premium (d) The real rate of interest

68. What is the real rate of interest if the nominal rate of interest is 15%, the IF is 3%, the DRP is 3%, the MRP is 3%,

and the LP is 2%?

(a) 3% (b) 4% (c) 5% (d) None of the above

69. The risk-free interest rate is composed of?

(a) An inflation premium and a default risk premium (b) A default risk premium and a maturity risk premium

(c) A real rate of interest and a liquidity premium (d) A real rate of interest and an inflation premium

70. When investors expect __________ inflation rates they will require __________ nominal interest rates so that a real

rate of return will remain after the inflation?

(a) Higher, lower (b) Higher, higher (c) Lower, higher (d) None of the above

71. With continuous compounding at 8 percent for 20 years, what is the approximate future value of a Rs. 2,000?

(a) Rs. 152,000.4 (b) Rs. 199,061.2 (c) Rs. 191,270.5 (d) Rs. 91,524.8

72. If the nominal rate of interest is 10%, the real rate of interest is 3%, the default premium is 3%, the liquidity

premium is 0.5%, and the maturity premium is 1.5%, then the inflation premium must be ______?

(a) 2.0% (b) 2.5% (c) 3.0% (d) None of the above

73. ___________________ states that interest rates are a function of the supply and demand for loanable funds?

(a) The expectations theory (b) The loanable funds theory

(c) The liquidity preference theory (d) The market segmentation theory

74. If the nominal rate of interest is 10%, the risk-free rate of interest is 3%, the default premium is 3%, the liquidity

premium is 0.5%, and the maturity premium is 1.5%, then the inflation premium must be ______?

(a) 2.0% (b) 2.5% (c) 3.0% (d) None of the above

75. The relationship between interest rates or yields and the time to maturity for debt instruments quality is called?

(a) The yield to maturity (b) The term structure of interest rates

(c) The maturity risk premium (d) The expectations hypothesis

76. Three theories commonly used to explain the term structure of interest rates include all of the following except?

(a) The default risk theory (b) The expectations theory

(c) The market segmentation theory (d) The liquidity preference theory

77. ______________ occurs during economic expansions when demand for goods and services is greater than supply?

(a) Administrative inflation (b) Speculative inflation

(c) Cost-push inflation (d) Demand-pull inflation

78. If the stated or nominal interest rate is 10 percent and the inflation rate is 5 percent, the differential compounding

rate would be ________ percent?

(a) Ten (b) Five (c) Two (d) Fifteen

79. The future value of Rs. 2,000 invested at 6% in 3 years would result in a value of?

(a) Rs. 2,000 (b) Rs. 6,362 (c) Rs. 2,382 (d) None of the above

Finance


Unit 2

80. An increase in the supply for loanable funds accompanied by a decrease in demand will cause interest rates to?

(a) Decrease (b) Increase (c) Stay the same (d) Not enough information to tell

81. Ali puts Rs. 1,000 in a savings passbook that pays 4% compounded quarterly. How much will he has in his account

after five years?

(a) Rs. 1,200.50 (b) Rs. 1,220.20 (c) Rs. 1,174.80 (d) Rs. 1,217.50

82. You put Rs. 2,000 in an IRA account at Northern Trust. This account pays a fixed interest rate of 8% compounded

quarterly. How much money do you have in five years?

(a) Rs. 2,914 (b) Rs. 2,938 (c) Rs. 2,972 (d) Rs. 2,999

83. Mr. Noman deposits Rs. 5,000 in a five-year certificate of deposit paying 6% compounded semi-annually. How

much will he has at the end of the five-year period?

(a) Rs. 6,720 (b) Rs. 6,690 (c) Rs. 6,596 (d) Rs. 6,910

84. For positive interest rates, the future value interest factor is

(a) Sometimes negative (b) Always greater than 1.0

(c) Always less than 0 (d) Never greater than 25

85. Inflation caused by an increase in the money supply is called?

(a) Demand-pull inflation (b) Cost-push inflation

(c) Administrative inflation (d) A combination of administrative and speculative inflation

86. Suppose you were going to save Rs. 1,000 per year for three years at a 10% interest rate compounded annually, with

the first investment occurring today. What would be the future value of this investment?

(a) Rs. 2,124 (b) Rs. 2,310 (c) Rs. 3,641 (d) Rs. 3,812

87. What would be the future value of a loan of Rs. 1,000 for two years if the bank offered a 10% interest rate

compounded semiannually?

(a) Rs. 1,720 (b) Rs. 1,960 (c) Rs. 1,200 (d) Rs. 1,216

88. When the amount earned on a deposit has become part of the principal at the end of a specified time period the

concept is called?

(a) Discount interest (b) Compound interest (c) Primary interest (d) Multi interest

89. If the interest rate is zero, the future value interest factor equals ________?

(a) -1.0 (b) 0.0 (c) 1.0 (d) 2.0

90. Rs. 100 is received at the beginning of year 1, Rs. 200 is received at the beginning of year 2, and Rs. 300 is received

at the beginning of year 3. If these cash flows are deposited at 12 percent, their combined future value at the end of

year 3 is ________?

(a) Rs. 1,536 (b) Rs. 727 (c) Rs. 672 (d) Rs. 1,245

91. The future value of Rs. 200 received today and deposited for three years in an account which pays semiannual

interest of 8 percent is ________?

(a) Rs. 253 (b) Rs. 252 (c) Rs. 158 (d) Rs. 135

2. unit 2 tvm

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