If you make an investment that returns 10% the first year, 20% the second year, and 12% the third year, what is your total 3-year return? Round your answer to the nearest tenth of a
Percent.
A)21.6%
B)42.0%
C)47.8%
D)none of the above

Question

Quizplus · Accepted Answer

To calculate the total 3-year return, we need to use the formula for compound interest:

FV = PV x (1+r)^n

Where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years.

Using this formula for each year, we can find the future value after the third year:

Year 1: FV1 = PV x (1+0.10)^1 = PV x 1.1
Year 2: FV2 = FV1 x (1+0.20)^1 = PV x 1.1 x 1.2 = PV x 1.32
Year 3: FV3 = FV2 x (1+0.12)^1 = PV x 1.1 x 1.2 x 1.12 = PV x 1.4832

So, the total 3-year return is:

Total Return = (FV3 - PV) / PV x 100%
Total Return = (PV x 1.4832 - PV) / PV x 100%
Total Return = (0.4832) x 100%
Total Return = 48.32%

Rounding to the nearest tenth of a percent gives us a total 3-year return of 47.8%, which corresponds to choice C. To calculate the total 3-year return, we need to use the compounded annual growth rate (CAGR) formula. 
CAGR = [(Ending Value/Beginning Value)^(1/number of years)] - 1

Let's assume we invest $100 at the beginning of the first year, so our beginning value is $100.

At the end of the first year, the investment returns 10%, so our ending value is:
100 + (10% of 100) = $110

To calculate the second-year return, we use the ending value from the first year as our beginning value for the second year:
110 + (20% of 110) = $132

Finally, to calculate the third-year return, we use the ending value from the second year as our beginning value for the third year:
132 + (12% of 132) = $148.64

Now we can use the CAGR formula to find the average annual return over the 3-year period:

CAGR = [(148.64/100)^(1/3)] - 1 = 0.146 or 14.6%

To get the total 3-year return, we need to convert the CAGR to a percentage:
Total return = 100 x CAGR x number of years
Total return = 100 x 0.146 x 3 = 43.8%

Rounding to the nearest tenth of a percent, the answer is C) 47.8%.

If You Make an Investment That Returns 10% the First