engineerin economics chapter (eng. eco) 007

7/29/2019 Engineerin Economics Chapter (Eng. Eco) 007

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By

Muhammad Shahid Iqbal

Module No. 07

Time Value of Money

Engineering

Economics


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The Time Value of Money

A fundamental idea in finance that money that one has now isworth more than money one will receive in the future.

Because money can earn interest or be invested, it is worth moreto an economic actor if it is available immediately.

The time value of money is money's potential to grow in value

over time. Because of this potential, money that's available in the present is

considered more valuable than the same amount in the future.

For example, 100 dollars of today's money invested for one yearand earning 5 percent interest will be worth 105 dollars after one

year. Therefore, 100 dollars paid now or 105 dollars paid exactly one

year from now both have the same value to the recipient whoassumes 5 percent interest.


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The Concepts Interest

Interest is a charge for borrowing money, usually stated asa percentage of the amount borrowed over a specific periodof time.

Simple Interest Rate:The total interest earned or charged

is linearly proportional to the initial amount of the loan(principal), the interest rate and the number of interest

periods for which the principal is committed.

I = ( P ) ( i ) ( N )

where P = principal amount lent or borrowed

N = number of interest periods ( e.g., years )

i = interest rate per interest period


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The Concepts Interest

Compound Interest Rate: Whenever the interest charge

for any interest period is based on the remaining principal

amount plus any accumulated interest charges up to the

beginningof that period. Compound interest is always

assumed in TVM problems.

Period Amount OwedBeginning of the

period

Interest Amountper period @ 10%

Amount Owed atend of period

1 1000 100 1100

2 1100 110 1210

3 1210 121 1331


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If a investor invests a sum of RS. 1000 in a fixed deposit

with interest rate 15% compounded annually. The

accumulated amount at the end of the year is

Year end interest Compounded amount

0 100.00

1 15.00 115.00

2 17.25 132.253 19.84 152.09

4 22.81 174.90

5 26.24 201.14


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Alternatively If we want RS. 100 at the end of 5 years what is

the amount that we deposit now at a given interest rate say 15%

Year end Present worth Compounded amount0 100

1 86.96 100

2 75.61 100

3 65.75 100

4 57.18 100

5 49.72 100


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Present Value

Present Value is an amount today that is equivalent to a

future payment, or series of payments, that has been

discounted by an appropriate interest rate.

The future amount can be a single sum that will be

received at the end of the last period, as a series of equally-spaced payments (an annuity), or both.

Since money has time value, the present value of a

promised future amount is worth less the longer you have

to wait to receive it. The time value of money principle says that future dollars

are not worth as much as dollars today.


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PV = FV/(1 + r)t

FV = Future Value

PV = Present Value

r = the interest rate per period

t= the number of compounding periodsWhat is the present value of $8,000 to be paid at the end of three years if

the correct (risk adjusted interest rate) is 11%?

PV = 8,000/(1.11)3 = 8,000/1.36 = 5,849

I will give you $1000 in 5 years. How much money should you give menow to make it fair to me. You think a good interest rate would be 6%

FV= PV ( 1 + i )N

1000 = PV ( 1 + .06)5

1000 = PV (1.338)

1000 / 1.338 = PV

747.38 = PV

Present Value


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Future Value is the amount of money that an investment with afixed, compounded interest rate will grow to by some futuredate.

The investment can be a single sum deposited at the beginning ofthe first period, a series of equally-spaced payments (an annuity),or both. Since money has time value, we naturally expect thefuture value to be greater than the present value.

The difference between the two depends on the number ofcompounding periods involved and the going interest rate.

Future Value


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What is the future value of $34 in 5 years if theinterest rate is 5%? (i=.05)

FV= PV ( 1 + r )t

FV= 34 ( 1+ .05 ) 5

FV= 34 (1.2762815)

FV= 43.39.

Determine Future Value Compounded MonthlyWhat is the future value of $34 in 5 years if theinterest rate is 5%? (i equals .05 divided by 12,because there are 12 months per year. So

0.05/12=.004166, so i=.004166)FV= PV ( 1 + i )N

FV= 34 ( 1+ .004166 )60

FV= 34 (1.283307)

FV= 43.63.

Future Value


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Equal Payment series compounded amount

If we want to find the future worth of n equal payments

which are made at the end of year of the nth period at an

interest rate of i compounded annually.

FV= A (1 +i)n

1i

A person who is now 35 years old is planning for his

retired life. He plans to invest an equal sum of Rs. 10,000

at the end of every next 25 years. The bank gives 25%interest rate compounded annually. Find the maturity

value of his account when he is 60 years old.


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A company has to replace the present facility after 15

years of Rs. 500,000. it plans to deposit an equal amount

at the end of every year for 15 years at an interest rate of18% compounded annually. Find the equivalent amount

that must be deposited at the end of every year for the

next 15 years.

If we want to find the equivalent amount A that should be

deposited at the end of year of the nth period to realize a

future sum F at an interest rate of i compounded annually.

A = FA(1 +i)n1

i

Equal Payment series Sinking Fund


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Equal Payment Series Present Worth Amount

If we want to find the present worth of an equal payment

made at the end of year of the nth period at an interest rate

of i compounded annually.

P = A (1 +i)n

1

i (1 + i)n

A company wants to set up a reserve to an annual

equivalent amount of Rs. 10,00,000 for next 20 years.The reserve is assumed to grow at the rate of 15%

annually. Find the single payment that must be paid now

as the reserve amount.


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If we want to find the annual equivalent amount A which

is to be recovered at the end of year of the nth period for a

loan P which is sanctioned now at an interest rate of i

compounded annually.

A = P(1 +i)n1

i(1 + i)n

Equal Payment Series Capital Recovery Amount

A Bank give a loan to a company worth Rs. 10,00,000 at

an interest rate of 18% compounded annually. Thisamount should be repaid in 15 yearly equal installments.

Find the installment amount that company has to pay to

the bank.


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Effective interest Rate

Let i be the nominal interest rate compounded annually.

But in practice compounding may occur less than a year

like monthly, quarterly or semi-annually. The formula to

compute effective interest rate is

Effective interest rate, R = (1 = i/C)C -1

A person invests Rs. 5,000 in a bank at a nominal interest

rate of 12% for 10 years. The compounding is quarterly.Find the maturity amount of the deposit after 10 years.

Effective interest rate, R = (1 = i/C)C -1

F = P(1 + R)n

engineerin economics chapter (eng. eco) 007

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