Question

Suppose one year ago the price index was 120 and Maria purchased $20,000 worth of bonds. One year later the price index is 126. Maria redeems her bonds for $22,700 and is in a 40 percent tax bracket. What is Maria’s real after-tax rate of interest to the nearest tenth of a percent?

Question 10 options:

	a) 2.4 percent.
	b) 2.1 percent.
	c) 5.1 percent.
	d) 3.1 percent.

Hide hint for Question 10
Hint: Use the equation rat = i(1-T) – π. The right answer is 3.1% but I would like to know the steps to get this answer

Answer 1

Price index a year ago = 120

Price index a year later = 126

Rate of inflation (ℼ) = (126-120) / 120 x 100 = 5% (0.05)

Maria redeemed her $20,000 worth bonds for $22,700 a year later.

Nominal interest rate on her bonds = (22,700-20,000) / 20,000 x 100 = 13.5% (0.135)

Real after-tax rate of interest: r(at) = i(1-T) - ℼ

Real after-tax rate of interest = 0.135(1-0.4) – 0.05

R(at) = (0.135*0.6) – 0.05

R(at) = 0.081 – 0.05 = 0.031

Real after-tax rate of return = 3.1% (0.031 x 100)

d) 3.1 percent.

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