What nominal interest rate should I charge based on inflation?

You are lending $100 to your roommate for a year. You both agree that you should earn a 5% real rate of return for the year.





a. If you make the loan in the base year, and you expect the inflation rate to be 2% over the year, what nominal rate of interest should you charge your roommate?








b. If you charge the interest rate you determined in part a, but the actual inflation rate was 5%, what was your real rate of return on the loan?|||a)


Ex Ante:


[Simple solution:]


Nominal interest = Real+Inflation = 5%+2% = 7%





[Right solution:]


(1+i) = (1+r) x (1+蟺) = 1.05 x 1.02 = 1.071


i = (1.05 x 1.02) - 1.00 = 0.071 = 7.1%





b)


Ex Post:


[Simple solution:]


Nominal interest = Real+Inflation


Real interest = Nominal - Inflation = 7% - 5% = 2%





[Right solution:]


(1+r) = (1+i) / (1+蟺) = 1.071 / 1.05 = 1.02


i = 1.02 - 1.00 = 0.02 = 2%