Question

You are planning on taking a loan for $9 ,000. You will repay the loan in annual payments over the next 5 years and the loan has a stated interest rate of 9%. For the very last payment on your loan, how much of this is repayment of principal? Enter your answer to the nearest dollar. Do not use $ or , signs in your answer. Enter your answer as a positive number. For example, if the loan payment is $400.87 of which $30.17 is interest and $370.70 is principal, your answer is that 370,70 is the repayment of the loan. Then, enter 371 as your answer in the space provided.

Answer 1

2123

Explanation:

You want to know the amount paid to principal in the last payment of a loan for $9000 at an interest rate of 9%, paid annually over 5 years.

Loan payment

The amount of the payment due is found using the formula ...

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

where P is the principal amount of the loan at annual rate r for t years with n payments per year.

The payments on this loan are ...

A = 9000(0.09)/(1 -1.09^-5) ≈ 2313.83

Future value

After 4 payments the remaining principal balance is ...

A = 9000·1.09^4 -2313.83(1.09^4 -1)/0.09 ≈ 2122.79

This remaining balance on the loan is the amount of principal in the last payment: $2123.

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