Question

Dylan is planning to purchase a new speaker system for his car that sells for $215.76 used. his bank can lend him the money at 18% for 24 months. His insurance company can lend him the money at 12% for 36 months. Determine the loan that will cost him less (simple interest)

Answer 1

First we have to obtain what's the interest of both:

$s=P\times i\times n$

Where s is the interest (simple), i is the interest rate (per year), P is the principal amount and n is the term of the loan in years.

For both loans the principal amount is the same P = $215.76

Then, the bank has an interest rate of 18%, so i = 0.18 and the loan is for 24 months, n = 2

$s_{bank}=215.76\times0.18\times2=77.67$

For the insurance company, the interest rate is 12%, i = 0.12 and the term of the loan is 36 months n = 3

$s_{i\text{ nsurance}}=215.76\times0.12\times3=77.6736$

The bank loan will cost him less than the insurance company loan