Question

In: Finance

A student takes out a loan of ​$1,900 at the beginning of each semester​ (semi-annually) for...

A student takes out a loan of ​$1,900 at the beginning of each semester​ (semi-annually) for 13 semesters to pay for college. The loan charges 7.6​% interest compounded semiannually. The student graduates after the 13 semesters and refinances the loan to a lower 6.9​% rate compounded monthly with monthly payments ​(made at the end of each​ month) for 120 months. Find the monthly payment and the total interest paid.

The monthly payment is

​$_____.

​(Round to the nearest cent as​ needed.)

The total amount of interest paid is.

​$_____.

​(Round to the nearest cent as​ needed.)

Solutions

Expert Solution

Student take a loan of $ 1900 at the beginning of each semester, for 13 semesters. Calculating the future value of loan after 13 semesters.

Where, C= Periodic loan amount = $1900

r = Periodic Interest rate = 7.6%/2 = 3.8%

n= no of periods = 13

Future Value = $ 32381.64

So, the value of loan after 13 semesters = $ 32,381.64

Now, Student refinances the loan at lower rate of 6.9%, Calculating the monthly Payments:

Where, P= Loan amount = $ 32,381.64

r = Periodic Interest rate = 6.9%/12 = 0.575%

n= no of periods = 120

Monthly Payment = $ 374.31

So, The monthly payment is $ 374.31

Total Interest Paid = ($374.31*120)-$32381.64

Total Interest Paid = $ 12,535.56


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