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.

Answer 1

The answer would be Loan A

even though she'll pay more per month, with the others she'll pay be paying more by the time she as payed it off due to having to pay interest over a longer period of time

Answer 2

Loan A is the cheapest.

Explanation:

The different loan plans are showed in the image attached.

Loan A: 12 months of duration with 9.50%.

Loan B: 24 months of duration with 8.75%.

Loan C: 36 months of duration with 7.75%.

Loan D: 48 months of duration with 6.60%.

Now, all loans are compouneded monthly. Let's the compound interest formula

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

Loan A:

`A=2500(1+(0.095)/(12) )^(12(1))\\A=2,748.12`

Loan B:

`A=2500(1+(0.095)/(24) )^(24(2)) \\A=2500(1.004)^(48)\\ A=3,028.02`

Loan C:

`A=2500(1+(0.095)/(36) )^(36(3)) \\A=2500(1.003)^(108)\\ A=3,454.94`

Loan D:

`A=2500(1+(0.095)/(48) )^(48(4))\\ A=2500(1.002)^(192)\\ A=3,668.95`

Now, if you compare, you will observe that Loan A offer the cheapest result for Judy.

Therefore, Judy should use the Loan A plan.