Question

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.

Answer 1

To find the athlete's salary for year 7 of the contract, apply a 4% annual increase to the previous year's salary starting from year 2. The athlete's salary for year 7 is approximately $3,836,192.

Step-by-step explanation:

To find the athlete's salary for year 7 of the contract, we need to calculate the annual increase for each year from year 2 to year 7 and apply it to the starting salary of $3,000,000 for year 1.

In year 2, the salary is 1.04 times the previous year's salary, so the salary for year 2 is $3,000,000 * 1.04 = $3,120,000.

In year 3, the salary is 1.04 times the previous year's salary, so the salary for year 3 is $3,120,000 * 1.04 = $3,244,800.

Following the same pattern, we can calculate the salaries for years 4, 5, 6, and 7:

In year 4: $3,244,800 * 1.04 = $3,379,392

In year 5: $3,379,392 * 1.04 = $3,523,027.68

In year 6: $3,523,027.68 * 1.04 = $3,675,348.11

In year 7: $3,675,348.11 * 1.04 = $3,836,191.72

Therefore, the athlete's salary for year 7 of the contract is approximately $3,836,192.

Answer 2

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