Question

Suppose that $14,000 is deposited for eight years at 4% APR. Calculate the interest earned if interest is compounded weekly. Round your answer to the nearest cent.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To calculate the interest earned when interest is compounded weekly, we use the formula:

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

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

In this case:
P = $14,000
r = 0.04
n = 52 (weekly compounding)
t = 8

A = $14,000(1 + 0.04/52)^(52*8)
A = $14,000(1 + 0.000769231)^(416)
A = $14,000(1.000769231)^(416)
A = $14,000(1.37581467)
A = $19,261.41

Interest earned = A - P = $19,261.41 - $14,000 = $5,261.41

Therefore, the interest earned if $14,000 is deposited for eight years at 4% APR with weekly compounding is $5,261.41.