Question

Suppose that $13,000 is deposited for five years at 5% APR. Calculate the interest earned if interest is compounded semiannually. Round your answer to the nearest cent.

Answer 1

[AI-generated answer — Bot GPT 3.5]

The formula for compound interest is A = P(1 + r/n)^(nt), where:

A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = annual interest rate (decimal)
n = number of times that interest is compounded per year
t = time the money is invested for in years

In this case:
P = $13,000
r = 0.05
n = 2 (compounded semiannually)
t = 5

A = 13000(1 + 0.05/2)^(2*5)
A = 13000(1 + 0.025)^10
A = 13000(1.025)^10
A = 13000(1.28008416359)
A = 16641.093125

Interest earned = A - P
Interest earned = $16641.09 - $13000
Interest earned = $3641.09

Therefore, the interest earned if interest is compounded semiannually is $3641.09.