Question

Publicity agents for the Detroit Felines announce the signing of a new second-string quarterback, Archie Parabola. They say that the contract is worth $1,000,000 and will be paid in 20 installments of $50,000 per year starting one year from now and with one installment each year thereafter until all 20 installments have been paid. The contract contains a clause that guarantees Parabola will get all of the money even if he is injured and cannot play a single game. Sports writers declare that Archie has become an "instant millionaire." The interest rate is 10%. 

Archie's sister, Gina, who majored in economics, explains to Archie that he is not a millionaire. How much is Archie's contract worth at the time he signed it? (Give your answer to two decimal places.)

What would be the present value of Archie's contract if the $50,000 annual payments continued forever? 

Answer 1

1.

Present worth of contract$= 50000\times (\frac{P}{A},10\%,20)$

$= 50000 \times \frac{((1 + 0.1)^{20}-1)}{(0.1\times(1 + 0.1)^{20})}$

$= 50000 \times \frac{((1.1)^{20}-1)}{(0.1\times (1.1)^{20})}\\ = 50000 \times 8.51356372$

= 425678.19

2

Present worth of contract = $\frac{50000 }{ 0.1 }= 500000.00$