Question

Imagine you borrow $1,100 from your roommate, agreeing to pay her back $1,100 plus 7 percent nominal interest in one year. Assume inflation over the life of the contract is expected to be 3.59 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? (Round answers to 2 decimal places, e.g. 12.25.)

Answer 1

Answer:

Dollar amount that you have to pay =  $1.179,52    

Dollar amount of interest results of real rate = $40,03

Explanation:

First of all, you have to convert the annual interest rate to annual efective rate with the next procedure:

a) transform annual interest rate to monthly interest rate:

Monthly interest= (7%/12) = 0,58%

b) Now you have to convert to  annual efective rate

Annual effective : =((1+0,58%)^(12))- 1 = 7,23%

Now that you has this rate, you can calculate how much money you have to pay at the end of the year with the formula of future value:

FV= amount monye borrowed *(( 1+7,23%)^(1))

FV $1.100 *(1+7,23)

FV=  $1.179,52    

Secondly, you need to have to do the same  procedure with the inflation

FV= amount monye borrowed *(( 1+3,59%)^(1))

FV $1.100 *(1+3,59%)

FV=  $1.139,49

Now if you have to make the next operation and find the difference between the amount of the value that you have to pay to your friend and substract the calculous

amount of the interest payment is the result of the real rate

$1.179,52 - $1.139,49 =  $40,03