Your recently departed rich, eccentric uncle has left for you in his will a large sum of money. Unfortunately, rather than giving you this sum of money immediately, he has instructed the executor of the will to pay you $10,000 in one year. This payment is to grow by 9% each year and to be made each year forever. If the appropriate discount rate is 10%, how much have you actually inherited?

Question

Quizplus · Accepted Answer

The present value of a perpetuity is the annual payment divided by the discount rate minus the growth rate. In this case, the annual payment is $10,000, the discount rate is 10%, and the growth rate is 9%. Therefore, the present value of the inheritance is $10,000 / (0.10 - 0.09) = $1,000,000.

Your Recently Departed Rich, Eccentric Uncle Has Left for You