Question

From the standpoint of the lender, mortgages involve investing dollars today and receiving dollars back in the future. Due to the effects of inflation over time, the lender will be paid back in “cheaper” dollars in the future. Consider a 15-year 7% mortgage that can be repaid with 15 annual payments of $18,000. Find the adjusted total amount paid by the borrower over this 15-year period on “real dollars”, if the annual rate of inflation over this 15-year period is 3.2%. Answer to the nearest dollar.

Answer 1

Given:
Loan amount	Not Given
Loan Duration (Years)	15
Interest Rate	7%
No of EMI for Repayment	15
EMI Amount	$18,000

First Step: We need to calculate the total amount that has been paid by the borrower to the lender at the end of 15 Years.

Total of all EMI Payments in Nominal Terms = $18,000*15 years = $270,000.

After paying $270,00, the borrower has paid off entire loan and interest on it.

This is the Nominal Value of the payment.

Step 2: Calculate Real Value of Total Amount Paid.

Since the borrower has paid a fixed amount of $18,000 every year for 15 years , we can discount the value using an annuity.

The discount rate for this will be the inflation rate = 3.2%

Time period = 15 years

Using the PV Function on your calculator, you get:

PV = $ 211,807.02

Conclusion:

A payment of $270,000 spread over 15 years with an annual inflation rate of 3.2% equates to a real value of $ 211,807 as on date of lending.