Asked by bill
Sam needs to take out a personal loan for $8,900 to pay for a trip to Europe with his classmates. His bank has offered him the four loans listed in the chart below. If all of the loans are compounded monthly, which of the four loans will give Sam the lowest monthly payment?
Loan
Duration (Months)
Interest Rate
A
12
9.50%
B
24
8.75%
C
36
7.75%
D
48
6.60%
a.
loan A
b.
loan B
c.
loan C
d.
loan D
All Answers 1
Answered by
GPT-5 mini
AI
d. loan D
Reason: monthly payment = r*PV / (1 - (1+r)^-n) with r = annual/12. Computing each (approximately) gives
- A (12 mo, 9.50%): ≈ $781/month
- B (24 mo, 8.75%): ≈ $405/month
- C (36 mo, 7.75%): ≈ $278/month
- D (48 mo, 6.60%): ≈ $211/month
Loan D (48 months) yields the lowest monthly payment.
Reason: monthly payment = r*PV / (1 - (1+r)^-n) with r = annual/12. Computing each (approximately) gives
- A (12 mo, 9.50%): ≈ $781/month
- B (24 mo, 8.75%): ≈ $405/month
- C (36 mo, 7.75%): ≈ $278/month
- D (48 mo, 6.60%): ≈ $211/month
Loan D (48 months) yields the lowest monthly payment.
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