Student Loan Debt Question

Question

Here is the question:

 

A student takes on $30,000 of debt in September 1 of 2016 at an annual interest rate of 8%. She makes no payments while in school. On November 1, 2019 she prepares to start repaying her debt on a 30-year repayment cycle, and the payment size is calculated. The first payment is made on December 1, 2019; the last one on November 1, 2049.

 

How much money will this person owe as of November 1, 2019? Round up to the nearest
penny

 

I know that the formula to find the new principal is f=p * (1+y)ⁿ where p is the principal, y is the interest rate, and n is the number of years. The question I have specifically is would I input 3 for n or 3.1666666667 because 3 years and 2 months pass by between September 1, 2016 and November 1, 2019?

 

Thanks

 

Answer 1

Assuming that the interest is compounded monthly, the answer would be:

 

30000 * (1 + .08/12)^38  since there are 38 months from 9/1/16 to 11/1/19

 

Answer is 38616.91 rounded up.