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.
Accepted Solution
A:
Answer: the athlete's salary for year 7 of the contract is $3795957Step-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-1Where Tn is the salary for the nth yeara is the salary for the first yearr is the rate at which the salary is increasing. Soa = 3,000,000n = 7r = 1.04We want to determine T7. It becomesT7 = 3000000 × 1.04^(7-1)T7 = 3000000 × 1.04^6Tn = $3795957