Last year, you purchased a stock at a price of $53.60 a share. Over the course of the year, you received $1.50 in dividends and inflation averaged 2.9%. Today, you sold your shares for $55.90 a share. What is your approximate real rate of return on this investment?

A) 4.2%
B) 7.1%
C) 7.9%
D) 8.6%
E) 10.0%

Question

Akshay Kandwal · Accepted Answer

Final Answer : A, Explanation :   The real rate of return adjusts the nominal return for the effects of inflation. First, calculate the nominal return:   Nominal Return = Ending Value + Dividends − Beginning Value Beginning Value  	ext{Nominal Return} = \frac{	ext{Ending Value} + 	ext{Dividends} - 	ext{Beginning Value}}{	ext{Beginning Value}}  Nominal Return = Beginning Value Ending Value + Dividends − Beginning Value ​     Nominal Return = 55.90 + 1.50 − 53.60 53.60 = 3.80 53.60 ≈ 0.0709  or  7.09 %  	ext{Nominal Return} = \frac{55.90 + 1.50 - 53.60}{53.60} = \frac{3.80}{53.60} \approx 0.0709 	ext{ or } 7.09\%  Nominal Return = 53.60 55.90 + 1.50 − 53.60 ​ = 53.60 3.80 ​ ≈ 0.0709  or  7.09%   Then, adjust for inflation using the formula:   Real Rate of Return = 1 + Nominal Rate 1 + Inflation Rate − 1  	ext{Real Rate of Return} = \frac{1 + 	ext{Nominal Rate}}{1 + 	ext{Inflation Rate}} - 1  Real Rate of Return = 1 + Inflation Rate 1 + Nominal Rate ​ − 1     Real Rate of Return = 1 + 0.0709 1 + 0.029 − 1 ≈ 1.0709 1.029 − 1 ≈ 0.0407  or  4.07 %  	ext{Real Rate of Return} = \frac{1 + 0.0709}{1 + 0.029} - 1 \approx \frac{1.0709}{1.029} - 1 \approx 0.0407 	ext{ or } 4.07\%  Real Rate of Return = 1 + 0.029 1 + 0.0709 ​ − 1 ≈ 1.029 1.0709 ​ − 1 ≈ 0.0407  or  4.07%   Therefore, the approximate real rate of return is 4.2%, rounding to the nearest tenth.

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