Question

You borrowed $15,000 from a student loan. If they charge 7.5% interest compounded monthly and you can pay back $300/month, how many years will it take for you to pay back the entire debt?

a.5.01 years
b.5.34 years
c.5.99 years
d.6.59 years
e.None of the above

Answer 1

It will take approximately 5.05 years to pay back the entire debt.

Step-by-step explanation:

To calculate the number of years it will take to pay back the entire debt, we need to find the number of payments needed. Let's break it down:

The loan amount is $15,000 and the monthly payment is $300.

The interest is compounded monthly at a rate of 7.5%.

First, we need to calculate the monthly interest rate by dividing the annual interest rate (7.5%) by 12:

Monthly interest rate = 7.5% / 12 = 0.625%

Next, we can use the loan payment formula:

Number of payments = log(PMT/(PMT - PV * rate), rate + 1)

Where:

PV = Loan amount ($15,000)

rate = Monthly interest rate (0.625%)

Substituting the values into the formula, we get:

Number of payments = log(300/(300 - 15000 * 0.00625), 0.00625 + 1)

Using a calculator, we find that the number of payments is approximately 60.6 months.

To convert this to years, we divide by 12:

Number of years = 60.6 months / 12 = 5.05 years

Hence, it will take approximately 5.05 years to pay back the entire debt.