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.
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.
To find the length of the loan in months, we need to convert the annual interest rate to a monthly rate.
First, we need to calculate the monthly interest rate by dividing the annual interest rate by 12 (number of months in a year):
Monthly interest rate = Annual interest rate / 12
= 10.2% / 12
= 0.85%
Next, we can calculate the total interest paid by using the formula:
Total interest = Principal * Interest rate * Time
Given that Susan paid $663 in interest and the principal loan amount was $5200, we can rearrange the formula to solve for Time:
Time = Total interest / (Principal * Interest rate)
= $663 / ($5200 * 0.85%)
Now, let's calculate:
Time = 663 / (5200 * 0.0085)
= 663 / 44.2
≈ 14.99
Therefore, the loan was approximately 14.99 months long.