Mikey cuts hair to pay for his tuition for college. Unfortunately, the cost of a

Question

Mikey cuts hair to pay for his tuition for college. Unfortunately, the cost of a haircut in his town hasn’t risen in years, and neither has his hourly wage. To make matters worse, the cover charge at his favourite club, Stages, keeps rising. He asks you to lend him $600, promising to repay you with interest at the end of one year. You try to convince him to stay home and do his work, but he doesn’t waiver. You decide to charge Mikey 5% interest, the same as the fixed rate on your student loan. At the end of the year, he repays you principal plus interest in full.

question:

Now use the ’exact’ growth rate formula to derive an expression for the expected real interest rate as

a function of only the nominal rate, i, and the expected inflation rate ^e: r = r(i, ^e)

Explanation / Answer

The fisher equation states that: 1+ Nominal rate = (1+inflation)*(1+real rate) Real rate = (1+nominal rate)/(1+inflation) -1 So the real return on the loan is: Principal * (1+ (1+nominal rate)/(1+inflation) -1) = principal* ((1+nominal rate)/(1+inflation))

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