Question

Nora needs to secure a loan for $6,000 and is considering two options.

Option 1: annual interest rate of 14% compounded monthly for 5 years

Option 2: annual interest rate of 16% compounded monthly for 6 years

Nora chooses the option that saves her interest.

Which option does she choose, and how much will she save in interest?

(1 point)
Nora chooses Option
. By doing so, she saves
in interest.

Answer 1

Option 1.

Work (rounded to cents):
- Option 1: i = 0.14/12 = 0.0116666667, N = 60
monthly payment = 6000*(i)/(1-(1+i)^-60) ≈ $139.61
total paid ≈ $139.61*60 = $8,376.47 → interest ≈ $8,376.47 − $6,000 = $2,376.47

- Option 2: i = 0.16/12 = 0.0133333333, N = 72
monthly payment = 6000*(i)/(1-(1+i)^-72) ≈ $130.17
total paid ≈ $130.17*72 = $9,371.99 → interest ≈ $9,371.99 − $6,000 = $3,371.99

Savings = $3,371.99 − $2,376.47 ≈ $995.52

So: Nora chooses Option 1 and saves about $995.52 in interest.