Macroeconomics 5th Edition by Olivier Blanchard

Exercise 1

Taxes, inflation, and home ownership
In this chapter, we discussed the effect of inflation on the effective capital-gains tax rate on the sale of a home. In this question, we explore the effect of inflation on another feature of the tax code-the deductibility of mortgage interest.
Suppose you have a mortgage of $50,000. Expected inflation is
and the nominal interest rate on your mortgage is i. Consider two cases.
a. What is the real interest rate you are paying on your mortgage in each case
b. Suppose you can deduct nominal mortgage interest payments from your income before paying income tax (as is the case in the United States). Assume that the tax rate is 25%. So, for each dollar you pay in mortgage interest, you pay 25 cents less in taxes, in effect getting a subsidy from the government for your mortgage costs. Compute, in each case, the real interest rate you are paying on your mortgage, taking this subsidy into account.
c. Considering only the deductibility of mortgage interest (and not capital-gains taxation), is inflation good for homeowners in the United States