Imagine you borrow $500 from your roommate, agreeing to pay her back $500 plus 7 percent nominal interest in one year. Assume inflation over the life of the contract is expected to be 4.25 percent. What is the total dollar amount you will have to pay her back in a year?

What dollar amount of the interest payment is the result of the real rate of interest?

a) What is the total dollar amount?

b) What is the interest payment?

a) The total dollar amount = $513.2

b) The interest payment = $13.20

Explanation:

Use following formula to calculate the real interest rate:

1 + Real Interest rate = (1 + Nominal Interest rate) / (1 + Inflation rate)

1 + Real Interest rate = (1 + 7%) / (1 + 4.25%)

1 + Real Interest rate = (1 + 0.07) / (1 + 0.0425)

1 + Real Interest rate = 1.07 / 1.0425

1 + Real Interest rate = 1.0264

Real Interest rate = 1.0264 - 1

Real Interest rate = 0.0264

Real Interest rate = 2.64%

a) The total dollar amount

A = P x (1 + r) ^n = 500 x (1 + 0.0264) ^1 = $513.2

b) The interest payment

Interest payment = $513.2 - $500 = $13.20