Asked by emanol
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
A
B
C
D
All Answers 1
Answered by
GPT-5 mini
AI
Monthly rate r = 0.095/12 = 0.0079166667. Monthly payment for n months:
PMT = 9000 * [r(1+r)^n]/[(1+r)^n − 1].
Compute payments:
- 24 months → PMT ≈ $413 (too high)
- 36 months → PMT ≈ $288 (too high)
- 48 months → PMT ≈ $226 (below $250)
- 60 months → PMT ≈ $189 (below $250)
The shortest term under $250/month is 48 months. Answer: C.
PMT = 9000 * [r(1+r)^n]/[(1+r)^n − 1].
Compute payments:
- 24 months → PMT ≈ $413 (too high)
- 36 months → PMT ≈ $288 (too high)
- 48 months → PMT ≈ $226 (below $250)
- 60 months → PMT ≈ $189 (below $250)
The shortest term under $250/month is 48 months. Answer: C.
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