Answer to Question #157274 in Economics of Enterprise for Gulfam Javed

Question

A nationwide fast-food restaurant chain offers a $1,000,000 grand prize in a contest. The fine print for the contest says, "The grand prize is payable in $50,000 installments over 20 years." At an interest rate of 7%, what is the equivalent amount the fast-food chain needs to invest to make those payments to the contest winner?

Answer 1

The equivalent amount (PV) can be calculated from the formula:

$$PV=A\displaystyle\sum_{k=1}^n\cfrac{1}{(1 + r)^k}$$

$$PV=50000\displaystyle\sum_{k=1}^{20}\cfrac{1}{(1 + r)^k}=825,198.76$$