Question

Bill Casler bought a $8000, 9-month certificate of deposit (CD) that would earn 8% annual simple interest. Three months before the CD was due to mature, Bill needed his CD money, so a friend agreed to lend him money and receive the value of the CD when it matured.

(a) What is the value of the CD when it matures?
(b) If their agreement allowed the friend to earn a 10% annual simple interest return on his loan to Bill, how much did Bill receive from his friend?

Answer 1

a

The value of the CD when it matures is
`V_(CD) =`$ 8,480

b

Bill receive from his friend
`z =`$8273.2

Explanation:

From the question we are told that

The price of the car is
`P =`$8000

The certificate of deposit is
`CD = 9 \ months`

The annual interest is
`a =`8%

The value CD when it matures can be mathematically represented as

`V_(CD) = P + (P * a * (t)/(12) )/(100)`

substituting values

`V_(CD) = 8000 + (8000 * 0.8 * (9)/(12) )/(100)`

substituting values we have

`V_(CD) =`$ 8,480

Let assume bill received z dollars from his friend

Now the total amount after three months which is the duration of the loan is mathematically evaluated as

`K = z + (z * 0.10 * (3)/(12) )/(100)`

Now since the amount after three month is equivalent to the value of CD as we are told from the question that Bill agreed his friend receives the CD as payback we have that

`K = 8480 = z + (z * 0.10 * (3)/(12) )/(100)`

=>
`8480 = z [1 + (1)/(40) ]`

=>
`z = (40)/(41) * 8480`

`z =`$8273.2