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Tim and Sally are taking out a personal loan to pay for their wedding expenses. The loan is for $9,000 and comes with an interest rate of 9.5% compounded monthly. The couple wants to pay the loan off as quickly as possible, keeping the monthly payments below $250. The lender offers repayment plans in 12-month increments. How long of a loan should they request?

A. 24 months
B. 36 months
C. 48 months
D. 60 months

Please select the best answer from the choices provided.

Answer :

Final answer:

Tim and Sally should request a 60-month loan.

Explanation:

To determine the length of the loan, we need to find a repayment plan that keeps the monthly payments below $250. To do this, we can use the formula for the monthly payment on a loan: PMT = (P * r) / (1 - (1 + r)^(-n)), where PMT is the monthly payment, P is the principal amount, r is the monthly interest rate, and n is the total number of payments. We can rearrange this formula to solve for n: n = -log(1 - (P * r) / PMT) / log(1 + r). Plugging in the values for this loan (P = $9,000, r = 9.5% / 12 = 0.00792, PMT = $250), we find that n ≈ 60.52. Since we are looking for the length of the loan in 12-month increments, the couple should request a 60-month loan (option d).

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