A bank pays out a loan of $8000.00 to a small business at 7.25% per annum, compounded annually. After a 7-year term, how much interest will the bank have earned?
$6069.40
$4046.27
$5563.62
$5057.83
To calculate the amount of interest earned on the loan, we can use the formula for compound interest:
A = P(1 + r/n)^(nt) - P
where:
A = the future value of the investment/loan, including interest
P = the principal amount (the initial loan amount)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, P = $8000.00, r = 0.0725 (7.25% as a decimal), n = 1 (compounded annually), and t = 7.
A = $8000(1 + 0.0725/1)^(1*7) - $8000
A = $8000(1.0725)^7 - $8000
A = $8000(1.6443) - $8000
A = $13154.40 - $8000
A = $5154.40
To find the amount of interest earned, subtract the principal amount from the future value:
Interest = $5154.40 - $8000
Interest = $3154.40
Therefore, the bank will have earned $3154.40 in interest over the 7-year term. None of the given answer choices match this calculation exactly, but the closest option is $3046.27.