\"A professional baseball player signs a contract for $159 million to play with

Question

"A professional baseball player signs a contract for $159 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:
$17 million each year for years 1 through 7.
$3.3 million each year for the next 10 years.
$1.0 million each year for the next 6 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 $17 million at the end of the first year. The player receives money for 23 years.
The player had previously rejected a contract that would have paid $147 million for 7 years in which the $147 million would be paid in 7 equal installments (i.e., $21 million per year). The first payment would be made at the end of the first year.
Assume the player will invest every dollar that he receives in an account that pays 5.7% interest compounded annually. Enter the amount in millions of dollars of the contract that would result in the most money at the end of 23 years for the player."

Explanation / Answer

compound interest formula(CI) =P(1+r/n)(nt)

where P is the principal amount deposited, r denotes annual interest rate, n denotes the times the interest is compounded and t means the number of years the money is deposited in the bank

Given that interest rate is 5.7% and compounded annually

here if the player joins with the first team that will give a sum of 159 million dollars with

a)17000000 dollars for one to seven years

CI=17000000(1=0.057/7)(7*7)

=25294768.84 us dollars

b)3300000 dollars for next 10 years

here we add 25294768.84 + 3300000=28594768.84 to get principal amount

CI=28594768.84(1+0.057/10)(10*10)

=50481424.67 dollars at the end of 17 years

c)1000000 dollars for the next 6 years

Now add the 1000000+50481424.67=51481424.67 is the principal amount in the end of 17th year

CI=51481424.679(1+0.057/6)(6*6)

=72356607.25 this is the total money the player get when he deposit all those money in the account and receives at end of 23 years(7+10+6) if he choose the first team in the question

if the player sign with the second team that pay 147 million dollars the total money received after 7 years will be

CI=21000000(1+0.057/7)(7*23)

=77495013.69 US dollars

from this, it is clear that if the player sign contract with the team(which he rejected) that pays 147 million dollars for seven years would result in the most money at the end of 23 years if he deposits in an account that pays 5.7% interest.

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