A professional athlete signs a four-year contract in which the earnings can be modeled by
c = 300,000 + 750,000t,
where t represents the year.
(a) Find the actual value of the athlete's contract.
=7200000
(b) Assuming an annual inflation rate of 4%, what is the present value of the contract? (Round your answer to two decimal places.)
To find the actual value of the athlete's contract, we can substitute the value of t into the given equation c = 300,000 + 750,000t. Since the contract is for four years, we will substitute t with 4:
c = 300,000 + 750,000 * 4
c = 300,000 + 3,000,000
c = 3,300,000
So, the actual value of the athlete's contract is $3,300,000.
To find the present value of the contract, we need to account for the annual inflation rate. The present value is the value of future cash flows in terms of today's dollars.
To calculate the present value, we can use the formula:
PV = FV / (1 + r)^n
Where PV is the present value, FV is the future value, r is the annual inflation rate (expressed as a decimal), and n is the number of years.
In this case, the future value (FV) is $3,300,000, the annual inflation rate (r) is 4% or 0.04, and the number of years (n) is 4.
PV = 3,300,000 / (1 + 0.04)^4
PV = 3,300,000 / (1.04)^4
PV = 3,300,000 / 1.16985856
PV = 2,818,559.56
Rounded to two decimal places, the present value of the contract is approximately $2,818,559.56.