I am considering a project which requires an immediate investment of $10 000 and yields a return in two years. If I expect the rate of inflation to be 15%, how big, in actual dollars, must the return be if my real rate of return on the project is to be 20%?
A)$13 500
B)$13 800
C)$14 400
D)$18 225
E)$19 044

Question

Quizplus · Accepted Answer

To achieve a real rate of return of 20% in the presence of 15% inflation, we use the formula for the real rate of return: $1 + real\ rate = \frac{1 + nominal\ rate}{1 + inflation\ rate}$. Rearranging to solve for the nominal rate gives us $nominal\ rate = (1 + real\ rate) \times (1 + inflation\ rate) - 1$. Plugging in the values gives us $nominal\ rate = (1 + 0.20) \times (1 + 0.15) - 1 = 1.38 - 1 = 0.38$ or 38%. To find the future value that gives a 38% return on a $10,000 investment, we calculate $10,000 \times (1 + 0.38) = 10,000 \times 1.38 = $13,800$. However, this calculation does not correctly account for the compound effect of inflation over two years. The correct approach involves adjusting the desired real return to account for inflation over the investment period, then calculating the future value needed to achieve this adjusted return.Given a real rate of return of 20% and an inflation rate of 15%, we first adjust the real rate to find the equivalent nominal rate needed to overcome inflation. Over two years, the real value of the investment needs to grow by 20%, but this growth is on top of maintaining its value against inflation. The formula to find the future value including inflation and real growth is: $Future\ Value = Present\ Value \times (1 + nominal\ rate)^n$, where $n$ is the number of years.To find the nominal rate that incorporates both the desired real return and inflation, we use the formula that combines both factors: $1 + nominal\ rate = (1 + real\ rate) \times (1 + inflation\ rate)^n$. For a 20% real return over two years with 15% annual inflation, the calculation is more complex than initially outlined, requiring us to account for the compound effect of inflation.The correct calculation involves finding the future value that equates to a 20% real return after adjusting for inflation over two years. This involves calculating the equivalent nominal return that would be needed to achieve a 20% real return in the context of 15% inflation, then applying this rate over the investment period to determine the necessary future value. The correct future value that accounts for both the desired real return and the impact of inflation over two years is $19,044, making option E the correct answer.

I Am Considering a Project Which Requires an Immediate Investment