project 3_simple interest

PROJECT 3 : SIMPLE INTEREST

Group 3: Xuân Mai

Thảo Như Thanh Phương

Thanh Thảo Hoài Trâm

I. Simple Interest Content: 1. Relation from the definition 2. The future value of the capital Vo 3. The case of year duration 4. The periodic nominal rate 5. The case of duration calculated by

months 6. Interest paid in advance

1. Relation from the definition

i: the annual rate: capital

: interest

Remark: With the leap year, the denominators in the formula are 366.

Example 1:

On 15/9/2002, Bob borrows $10000 from a bank under the interest rate 6.42% How much is the interest if he repays his loan in full on 19/1/2003?

N= 126

INT= 10,000*(

2. The future value of the capital Vo

Example 2: in example 1, the value of his loan on 19/1/2003 is:

Or .(

= + INT = 10000 + 221,62= $10221,62

When n= 365 days , we have:

3. The case of year duration

Example 3: On 5/3/2006, Bob borrows $10000 from a

bank under the interest rate 5.24%. How much is the interest if he repays his

loan in full on 5/3/2007 ?

INT= 10,000 * 0.0524= 524

4. The periodic nominal rate

It can be written as with =

is called the periodic nominal rate associated with i in the periods of n days.

INT=

INT=

5. The case of the duration is calculated in months

Generally, the interest (INT) is computed by:

In which t is the periodic nominal rate. In particular:Months: t= in which the period is of n months

6. Interest paid in advance Interest paid at the beginning of the period.

Eg: On 15/9/2002, Bob borrowed $10,000 from banks under the interest rate 6.42%. He would repay it on 19/1/2003. How much did he receive if Bob paid the interest in advance?

Eg: On 15/9/2002, Bob borrowed $10,000 from banks under the interest rate 6.42%. He would repay it on 19/1/2003. How much did he receive if Bob paid the interest in advance?

N= 126

= 10,000*(1 -

Effective rate (t)= Real interest rate Eg: On Sep 15, 2002, Bob borrowed $10,000 from under

the interest rate 6.42%. He would repay it on 19/1/2003. Find the effective rate if

a. He paid the interest in advance.b. He paid the interest at the end.

N= 126= 10,000*(1 - = t= 6.5%

b. t= 6.42%

7. Which situation do we prefer? Effective rate (t)= Real interest rate Eg: On Sep 15, 2002, Bob borrowed

$10,000 from under the interest rate 6.42%. He would repay it on 19/1/2003. Find the effective rate if

a. He paid the interest in advance.b. He paid the interest at the end.

II. Bank Discount Content: 1. Promissory notes 2. Commercial discount 3. Rational discount

1. Promissory notes - A promissory note: a legal document one signs promising to

repay a debt.- 2 kinds of

promissorynote:

• Definitions:- V0: the value of the P. note at the date 0(actual value) - Vn: the face value of the note (maturity value)

The interest bearing

P.n.

Non-interest bearing

P.n.

2. Commercial discount:- is the discount which its interest is calculated on the

face value of the P. note.E= (Vn * n * i)/365

- Actual value: V0 = Vn - E= Vn *(1-n*i/365)

- The effective discount rate: is the simple rate of the financial operation in which the present value is the actual value of the note and the future value is its face value.

EX: On the April 5, 2006, a business sells to its bank a P. note of $2 000 with maturity date June 15, 2006. The discount rate of the bank is 5,25%. How much money does he receive & what is the effective discount rate?

•Solution: We have Vn = $2000, i=5,25%, n=71days- The discount is given by:

E= (2000* 71* 0,0525)/365 = $20,42-The business receives

V0 = 2000 – 20,42 = $1979,57-The effective discount rate t

1979,57*(1+ 71*t/365)= 2000-> t = 5,31%

* Note: the effective discount rate> the nomial simple rate.

3. Rational discount- is the discount that its interest is calculated

on the actual value of the promissory note.Er =(V0,r *n*i)/365 = Vn (n*i)/365

1+ (n*i)/365•Remark: Rational discount ≤ Commercial Discount (E ≤ Er )EX: Let us consider the rational discount to the situation of the foregoing example. How much money does he receive and what is the rational discount?

Solution:- The business recerives an amount of money

V0 = 2000/(1+71*0,0525/365)= $1979,78

- The rational discount isEr = 2000- 1979,78= $20,22

In conclusion: Commercial Discount

Rational discount

Compare

Face value $2000 $2000

Actual value V0 =$1979,57 Vo,r = 1979,78 Vo,r > V0

Discount E= $20,42 Er =$20,22 Er < E

PROBLEMS OF SIMPLE

INTEREST RATE

Question 1. On March 17,2007, Bob intend to sell to his bank 2

promissory notes of the same debtor, John. The first is of face value $40,000 and matures on April

21, 2007. The second is of face value $60000 and matures on May

20, 2007.How much does he get from the bank if the discount rate is of 7% ?

2. At the same time, March 17, 2007, John asks Bob to replace these 2 notes by an unique promissory note of face value $99940 which matures on May 6, 2007.

With the interest rate 7%, should Bob accept this proposal?

QUESTIONThe financial department of Bob’s company owns 2 promissory notes of the same debtor, Tom:

The first is of $75,000 which matures on July 27, 2007.

The second id of $132,000 which matures on September 6, 2007.

On July 27, 2007, Tom propose to replace the 2 above notes by an unique promissory note which matures on October 11, 2007.

Suppose that the discount rate is 6%. How much is the face value of the new promissory note?

QUESTIONA promissory note is of face value

$30,000 and of maturity date on May 30, 2007. Suppose that the discount rate is of 6,24%. On what date this note is equivalent to the promissory note of $30,216 which matures on July 10, 2007?

QUESTIONOn November 3, 2006, a businessman replace the

following 3 promissory notes: The first of face value $42,000 which matures

on November 22, 2006. The second of face value $60,000 which

matures on December 7, 2006. The third of face value $90,000 which matures

on March 8, 2007,by an unique promissory note of face value $198,500.

What is the maturity date of the unique note if the interest rate is 6,2% ?

QUESTIONBob owns the following 3 promissory notes:

The first of face value $14,000 and of maturity date on January 20, 2007,

The second of face value $28,000 and of maturity date on February 10, 2007,

The third of face value $42,000 and maturity date on June 8, 2007.

His bank discounts these 3 notes on December 20, 2006 with the total discount interest of $2,356.

How much is the discount rate ?

QUESTION1. On November 12, 2006, Bob’s company

sells to its bank the following 2 promissory notes:

The first is of face value: $13,900 and of maturity date on February 15, 2007,

The second is of face value: $13,640 and of maturity date December 10, 2006;

a) The company gets the same value for each note. Calculate the discount rate. b) Determine the face value of the unique promissory note with maturity date on January 15, 2007 which can be replaced these 2 above notes on November25, 2006 at the discount rate 7,8%.

2. Besides, on January 20, 2007, Bob’s company also sells another promissory note of face value $20,000 and of maturity date on April 29, 2007. The bank uses the discount rate of 7,8% and deducts $70 for the document fees.

Determine the effective rate of the discount.

THANK YOU FOR YOUR

ATTENTION !