Question

Bill Casler bought a $9000,9-month certificate of deposit (CD) that would earn 9.2% annual simple interest. (a) What is the value of the CD when it matures? $ (b) 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. 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.) $

(c) What annual simple interest rate did Bill Casler end up making on his investment? Round your answer to two decimal places. %

Answer 1

a) ı = prt = $9000 x 0.092 x 0.75 = $621

$9000 + $621 = $9621

b) I = Prt = $9000 x 0.092 x 0.5 = $414

$9000 + $414 = $9414

c) $621 (from part (a)) + $414 (from part (b)) = $1035

r = (I/P) x (1/t) = ($1035 / $9000) x (1/0.75) = 0.1537

So Bill Casler ended up making an annual simple interest rate of 15.37%.

Explanation:

(a) Using the formula for simple interest, we can find the value of the CD when it matures:

I = Prt

where I is the interest earned, P is the principal (the initial amount invested), r is the annual interest rate, and t is the time in years.

In this case, P = $9000, r = 0.092 (since 9.2% is the annual interest rate), and t = 9/12 (since the CD has a term of 9 months, or 0.75 years).

ı = prt = $9000 x 0.092 x 0.75 = $621

So the value of the CD when it matures is:

$9000 + $621 = $9621

(b) Three months before the CD was due to mature, it had been invested for 6 months, so the interest earned up to that point would be:

I = Prt = $9000 x 0.092 x 0.5 = $414

The value of the CD at this point would be:

$9000 + $414 = $9414

So Bill's friend lent him $9414. At the end of the 3-month period, the friend would earn:

I = Prt = $941.40

Therefore, the total amount owed to the friend at maturity is:

$9414 + $941.40 = $10355.40

(c) The total interest earned on the investment is:

$621 (from part (a)) + $414 (from part (b)) = $1035

The investment was for a total of 9 months, or 0.75 years, so the annual simple interest rate can be found by dividing the total interest by the principal and multiplying by the number of years:

r = (I/P) x (1/t) = ($1035 / $9000) x (1/0.75) = 0.1537

So Bill Casler ended up making an annual simple interest rate of 15.37%.