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Chapter 5: Problem 75

You can choose between two investments that mature at different times in the future. If you knew the rate of inflation, how would you decide which is the better investment?

Short Answer

Expert verified
To determine the better investment between two investments with different maturity times, consider the rate of inflation and calculate the real return on investment (ROI) for each option. First, find the future value (FV) of both investments using the formula \(FV = P(1 + r)^{t}\). Next, adjust the future values for the expected rate of inflation using the real return formula, \(Real \ ROI = \frac{(1 + nominal \ ROI)}{(1 + inflation \ rate)} - 1\). Finally, compare the real ROI of both investments. The investment with the higher real ROI is the better option, as it provides higher returns after accounting for inflation.

Step by step solution

01

Identify the given information for each investment

To compare the two investments, we need to know the principal (initial investment), interest rate, and the time period (years) until maturity for both options.
02

Calculate the future value of each investment

We can use the future value (FV) formula to determine how much each investment will be worth at the time of maturity. The formula for future value is: \(FV = P(1 + r)^{t}\) Where, FV is the future value, P is the principal (initial investment), r is the annual interest rate (as a decimal), t is the time period (in years). Calculate the future value for both investments using this formula.
03

Adjust the future values by the rate of inflation

Now that we have calculated future values, we need to adjust them by the expected rate of inflation. To do this, we use the real return formula: \(Real \ ROI = \frac{(1 + nominal \ ROI)}{(1 + inflation \ rate)} - 1\) Where, Real ROI is the real return on investment adjusted for inflation, Nominal ROI is the annual interest rate of each investment, Inflation rate is the expected rate of inflation (as a decimal). Calculate the real ROI for both investments using this formula.
04

Compare the real ROI of both investments

Now that we have the real ROI for both investments, comparing them will allow us to determine which is the better investment in terms of future purchasing power. The investment with the higher real ROI will be the better option since it means higher returns after accounting for inflation.

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