A professional baseball player signs a contract with a beginning salary of $3,000,000 for the first year and an annual increase of 4% per year beginning in the second year. That is, beginning in year 2, the athlete's salary will be 1.04 times what it was in the previous year. What is the athlete's salary for year 7 of the contract? Round to the nearest dollar.

Question

Mathematics

Kate Lang

28 June, 03:35

A professional baseball player signs a contract with a beginning salary of $3,000,000 for the first year and an annual increase of 4% per year beginning in the second year. That is, beginning in year 2, the athlete's salary will be 1.04 times what it was in the previous year. What is the athlete's salary for year 7 of the contract? Round to the nearest dollar.

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Karma · Answer 1

Answer: the athlete's salary for year 7 of the contract is $3795957

Step-by-step explanation:

The player signs a contract with a beginning salary of $3,000,000 for the first year and an annual increase of 4%. This means that the amount he gets each year is 1.04 times of the previous year's amount. The rate at which his salary increases is in geometric progression. The nth term of a geometric progression is expressed as

Tn = ar^n-1

Where

Tn is the salary for the nth year

a is the salary for the first year

r is the rate at which the salary is increasing. So

a = 3,000,000

n = 7

r = 1.04

We want to determine T7. It becomes

T7 = 3000000 * 1.04^ (7-1)

T7 = 3000000 * 1.04^6

Tn = $3795957