Answer: $40,146.75
Step-by-step explanation:
1) The loan amount is $30,000.00.
2) The interest rate is 6% per year.
3) The loan is compounded annually, which means the interest is added once a year.
4) The loan has a total of 10 annual payments, but the borrower paid off the loan after 5 years.
5) To calculate the amount needed to pay off the loan after 5 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial loan amount)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
6) Plugging in the values into the formula:
P = $30,000.00
r = 6% = 0.06 (as a decimal)
n = 1 (compounded annually)
t = 5 (since the loan was paid off after 5 years)
A = $30,000.00(1 + 0.06/1)^(1*5)
A = $30,000.00(1 + 0.06)^5
A = $30,000.00(1.06)^5
A = $30,000.00(1.338225)
A = $40,146.75
7) Therefore, the amount needed to pay off the loan after 5 years is $40,146.75.