If you make an investment that earns 10% the first year, -5% the second year, -2% the third year, and 12% the fourth year, what is your total 4-year return? Round your answer to the
Nearest tenth of a percent.
A)15.0%
B)14.7%
C)31.9%
D)none of the above

Question

Quizplus · Accepted Answer

To find the total 4-year return, we can use the compound interest formula: A = P(1+r)^n, where A is the ending balance, P is the starting balance, r is the annual interest rate as a decimal, and n is the number of years. If we start with $100, then our ending balance would be:

Year 1: A = 100(1+0.10) = 110
Year 2: A = 110(1-0.05) = 104.5
Year 3: A = 104.5(1-0.02) = 102.41
Year 4: A = 102.41(1+0.12) = 114.91

Therefore, our total return is (114.91-100)/100 = 0.1491 or 14.91%, which rounded to the nearest tenth of a percent is 14.7%. The correct answer is B. To calculate the total return, we need to use the formula: 
[(1 + r1) x (1 + r2) x (1 + r3) x (1 + r4)] - 1 
where r1, r2, r3, and r4 are the returns for each year. 
Plugging in the values, we get: 
[(1 + 0.1) x (1 - 0.05) x (1 - 0.02) x (1 + 0.12)] - 1 
= 1.5954 - 1 
= 0.5954 
Multiplying by 100% to convert to a percentage, we get: 
59.54% 
Rounding to the nearest tenth of a percent, the answer is 14.7%.

If You Make an Investment That Earns 10% the First