Investment X and Investment Y are both growing perpetuities with initial cash flow of $100. Both investments have the same interest rate (r). The present value of Investment X is $5 000, while the present value of Investment Y is $4 000. Which of the following is true?

Question

Quizplus · Accepted Answer

The present value of a perpetuity is calculated as the annual cash flow divided by the interest rate. Therefore, we can set up the equations:
$5,000 = \frac{100}{r}$
$4,000 = \frac{100}{r}$
Solving for r in each case gives us:
$r = \frac{100}{5,000} = 0.02$
$r = \frac{100}{4,000} = 0.025$
We can see that Investment Y has a higher interest rate, which means it has a higher growth rate. Therefore, choice B is correct.

Investment X and Investment Y Are Both Growing Perpetuities with Initial