\"A professional baseball player signs a contract for $158 million to play with

Question

"A professional baseball player signs a contract for $158 million to play with a team for 7 years. He and his team agree that the contract will be spread out so that the player is paid beyond the 7 years. The payment plan for the contract is as follows:
$18 million each year for years 1 through 7.
$3.4 million each year for the next 12 years.
$1.2 million each year for the next 8 years.
You should assume that the baseball team will pay the player annually at the end of each year and that he will receive the first $18 million at the end of the first year. The player receives money for 27 years.
If the interest rate is 5.4% compounded annually, how much does the baseball team need to deposit in year 0 in order to fully fund this contract? Express your answer in millions of dollars."

Explanation / Answer

Answer : According to the question, the payer is paid for 27 years. Now based on given payment plan of contract we can get the total paid amount to player by the baseball team in the following process.

Each year payment is $18 million for first 7 years. Therefore, in first 7 years total paid amount = (18 × 7) = $126 million.

Each year payment is $3.4 million for next 12 years. Therefore, in next 12 years total paid amount = (3.4×12) = $40.8 million.

Each year payment is $1.2 million for next 8 years. Therefore, in next 8 years total paid amount = (1.2 × 8) = $9.6 million.

Now, for total (7 + 12 + 8) = 27 years the total paid amount is (126 + 40.8 + 9.6) = $176.4 millions .

Given,

Interest rate (r) = 5.4% = 0.054; Time (t) = 27 years; Total paid amount (A) = $176.4 millions. We have to find out the initial deposited amount to fund the total paid amount of contract. Let, the initial deposited amount is P.

Now, the formula of total amount in anual compounding interest is as follows :

A = P (1 + r)^t

=> 176.4 = P (1 + 0.054)^27

=> 176.4 = P × 4.1

=> P = 176.4 / 4.1

=> P = 43.0 = $43 millions

Therefore, initially the baseball team has to deposit $43 millions to fund the total paid amount of contract.

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