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A borrower had a loan of $30,000.00 at 6% compounded annually, with 10 annual payments. Suppose the borrower paid off the loan after 5 years. Calculate the amount needed to pay off the loan The amount needed to pay off this loan after 5 years is $__________

User Injecteer
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1 Answer

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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.

User Mochalygin
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