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? (Round your answer to the nearest cent.)

Answer 1

Answer:

a) $8480

b) $8273.17

Step-by-step explanation:

1) Notation

P the principal amount = $8000

Time for maturity = 9 months

I = 8% = 0.08 the simple interest

2)Formulas to use

Future value with simple interest

$FV=P(1+i)$   (1)

Where i represent the annual rate of interest, on this case since we have on 1 year 12 months we can do this:

$i=\frac{8}{100}\frac{9}{12}=\frac{3}{50}$

3) Part a

Now we can replace in formula (1)

$FV=8000(1+\frac{3}{50})= 8480$

So then the value for the Certificate of deposit at the maturity would be $8480.

4)Part b

If the friend earns 10% annual simple interest, then the amount that  Bill will recieve would be the present value from formula (1) with a future value FV= 8480

If we solve PV from equation (1) we got

$PV=\frac{FV}{1+i}$ (2)

Where i would represent the following value

$i=0.1x\frac{3}{12}=\frac{1}{40}$

Since three months before the CD was due to mature, Bill needed his CD money, he just earns 3 months for the total of 12 in a year.

Then replacing into equation (2) we got:

$PV=\frac{8480}{1+\frac{1}{40}}=8273.17$