Suppose the nominal interest rate is rn and inflation is i. Assume 0 < rn < 1 and 0 < i < 1. Suppose the approximation that relates real interest rate to the nominal interest rate and inflation, rr = rn − i holds. Suppose t with 0 < t < 1 be the tax rate on interest.
A. Write a formula for the after tax interest rate R1 in an inflation protected tax system.
B. Write a formula for the after tax interest rate R2 when tax brackets do not provide relief from inflation.
C. Compare R1 and R2. How does the difference between the two change if inflation rate doubles?