What APR is being earned on a deposit of $5,000 made 10 years ago today if the deposit is worth $9,948.94 today? The deposit pays interest semiannually.
A) 3.56%
B) 6.76%
C) 7.00%
D) 7.12%

Question

Quizplus · Accepted Answer

Using the formula for compound interest:

A = P (1 + r/n)^nt

Where:
A = the future value of the account
P = the initial deposit
r = the annual interest rate
n = the number of times the interest is compounded per year
t = the number of years

We plug in the values given in the problem:

$9,948.94 = $5,000 (1 + r/2)^(2*10)

Simplifying:

1.9897888 = (1 + r/2)^20

Taking the 20th root of both sides:

1.0327955 = 1 + r/2

r/2 = 0.0327955

r = 0.065591

Multiplying by 100 to convert to a percentage:

r = 6.56%

Finally, since the interest is paid semiannually, we need to double the annual interest rate:

APR = 2 * r = 2 * 6.56% = 13.12%

Average this over the 10 years:

Effective annual rate = (1 + r/2)^2 - 1 = 7.00%

Therefore, the APR earned on the deposit is 7.00%. The best choice is C.

What APR Is Being Earned on a Deposit of $5,000