An infamous Bears quarterback just renegotiated his contract

An infamous Bears quarterback just renegotiated his contract for his next 5 seasons. The contract was for a total of $50 million, paid in equal installments of $10 million for each of the following five years. A wide receiver, envious of the quarterback, demanded his contract also be renegotiated. The wide receiver was able to obtain a $48.5-million package which included $11 million upfront (paid NOW) and $7.5 million annually for 5 years. Both claimed they got a better deal. Who actually did get a better deal? Assume an interest rate of 5% per year.

Solution

Let\'s assume that every year the quarterback will keep all the money earned...

First payment: ($10 million) + (0.05 x $10 million) = $10.5 million

Second payment: ($10 million) + (0.05 x $10 million) = $10.5 million

Third payment: ($10 million) + (0.05 x $10 million) = $10.5 million

Fourth payment: ($10 million) + (0.05 x $10 million) = $10.5 million

Fifth payment: ($10 million) + (0.05 x $10 million) = $10.5 million

TOTAL PAID = (5 x $10.5 million) = $52.5 million

First payment: ($11 million upfront + $7.5 million) + (0.05 x $18.5 million) = $19.425 million

Second payment: ($7,5 million) + (0.05 x $7.5 million) = $7.875 million

Third payment: ($7,5 million) + (0.05 x $7.5 million) = $7.875 million

Fifth payment: ($7,5 million) + (0.05 x $7.5 million) = $7.875 million

TOTAL PAID = ($19.425 million) + (4 * $7.875 million) = $50.925 million

Who actually did get a better deal? The person who proposed the 1^ST CASE!