Question

Judy needs to take out a personal loan for $2,500 for tuition assistance. Her bank has offered her one of the four loan packages outlined in the chart below. Determine which of the four loans will be cheapest for Judy in the long run. All interest rates are compounded monthly.

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

Answer 1

We compare total amount repaid for amortized monthly payments. Monthly rate r = (annual rate)/12, monthly payment
m = P * r / (1 − (1 + r)^(−n)), total paid = m * n (P = $2,500).

Calculations (rounded):

- Loan A: n = 12, r = 0.095/12 = 0.007916667
m ≈ $218.33, total ≈ $2,620

- Loan B: n = 24, r = 0.0875/12 = 0.007291667
m ≈ $113.74, total ≈ $2,730

- Loan C: n = 36, r = 0.0775/12 = 0.006458333
m ≈ $78.17, total ≈ $2,814

- Loan D: n = 48, r = 0.066/12 = 0.0055
m ≈ $59.36, total ≈ $2,849

The smallest total repaid is Loan A. Answer: a. loan A.