An amount of $27,000 is borrowed for 12 years at 3.25% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back? Use the calculator provided and round your answer to the nearest dollar.
per the usual formula, that would be
27000 * 1.0325^12
To calculate the amount that must be paid back, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (the amount that must be paid back)
P = the principal amount (the initial loan amount)
r = the annual interest rate (expressed as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $27,000, the annual interest rate (r) is 3.25% or 0.0325 as a decimal, the loan is compounded annually (n = 1), and the loan term (t) is 12 years.
Plugging these values into the formula, we have:
A = 27000(1 + 0.0325/1)^(1*12)
Using a calculator, we can evaluate this expression to find the final amount that must be paid back. Rounding the answer to the nearest dollar as instructed, we get:
A ≈ $37,099
Therefore, approximately $37,099 must be paid back to fully repay the loan.