Question

Susan took out a loan for $5200 and was charged simple interest at an annual rate of
10.2%. The total interest she paid on the loan was $663.

How long was the loan for, in months?
Do not round any intermediate computations.

Answer 1

We can use the formula for simple interest:

I = Prt

where I is the interest, P is the principal (the loan amount), r is the annual interest rate expressed as a decimal, and t is the time in years.

We can rearrange this formula to solve for t:

t = I / Pr

Plugging in the given values, we get:

t = 663 / (5200 x 0.102)
t = 12.5

So the loan was for 12.5 years. But the question asks for the time in months, so we need to convert:

12.5 years x 12 months/year = 150 months

Therefore, the loan was for 150 months.