A one-time gift to your college will provide $25,000 in scholarship funds next year with that amount increasing by 2 percent annually thereafter. If the discount rate is 5.5 percent, what is the current value of this perpetual gift?

Question

Quizplus · Accepted Answer

The current value of a perpetual gift that grows at a rate different from the discount rate can be calculated using the formula: $PV = \frac{C}{r - g}$, where $PV$ is the present value, $C$ is the initial cash flow, $r$ is the discount rate, and $g$ is the growth rate. Here, $C = \$25,000$, $r = 5.5\% = 0.055$, and $g = 2\% = 0.02$. Plugging these values into the formula gives: $PV = \frac{\$25,000}{0.055 - 0.02} = \frac{\$25,000}{0.035} = \$714,285.71$.

A One-Time Gift to Your College Will Provide $25,000 in Scholarship