A person invests in a fund earning interest at j₂ = 6%.The annual rate of inflation is 2% in year 1,2.5% in year 2,and 3.0% in year 3.What is the annual real interest rate,compounded once a year,earned over the 3-year period? A)3.42% B)3.47% C)3.50% D)3.59%

Question

Quizplus · Accepted Answer

1. Calculate the nominal interest rate for each year:
Year 1: 6% - 2% = 4%
Year 2: 6% - 2.5% = 3.5%
Year 3: 6% - 3% = 3%

2. Calculate the real interest rate for each year:
Year 1: (1+0.04)/(1+0.02)-1 = 1.961 - 1 = 0.961 = 96.1%
Year 2: (1+0.035)/(1+0.025)-1 = 1.0097 - 1 = 0.0097 = 0.97%
Year 3: (1+0.03)/(1+0.03)-1 = 1 - 1 = 0

3. Calculate the total real interest rate over the 3-year period:
(1+0.961)(1+0.0097)(1+0)^(1/3)-1 = 1.035 - 1 = 0.035 = 3.50%

Therefore, the annual real interest rate, compounded once a year, earned over the 3-year period is 3.50%. Therefore, the best choice is (C).

A Person Invests in a Fund Earning Interest at J2

A Person Invests in a Fund Earning Interest at J₂