Jack invested $1200 into an account for 5-years.The account paid interest at j₁ = 4% for the first 2-years and j₁ = 6% thereafter.If the annual inflation rate is 2% for each of these 5-years,what is the annual real rate of interest earned over the 5-years?

Question

Quizplus · Accepted Answer

First, we need to calculate the future value (FV) of the investment after 5 years.
For the first 2 years, the interest rate is 4%.
FV after 2 years = 1200 x (1+0.04)^2 = 1,324.16
For the remaining 3 years, the interest rate is 6%.
FV after 5 years = 1,324.16 x (1+0.06)^3 = 1,611.47

Next, we need to calculate the inflation-adjusted FV using the formula:
Inflation-adjusted FV = FV / (1+inflation rate)^n
where n is the number of years

In this case, n = 5 and the inflation rate is 2% for each year.
Inflation-adjusted FV = 1,611.47 / (1+0.02)^5 = 1,408.84

The real rate of return can be calculated using the formula:
Real rate of return = (Inflation-adjusted FV / initial investment)^(1/n) - 1

In this case, the initial investment is $1200 and n = 5.
Real rate of return = (1,408.84 / 1200)^(1/5) - 1 = 0.0313 or 3.13%

Therefore, the answer is B) 3.13%.

Jack Invested $1200 into an Account for 5-Years