### Home > INT3 > Chapter Ch10 > Lesson 10.2.1 > Problem 10-104

10-104.

Joe’s dad is only 40, but he is already planning for retirement. If he retires early at age 55, he will receive an annual pension starting at $30,000 that increases at a rate of 3% each year to account for inflation. If he waits until he is 65, his pension will be a percentage of his salary at that time. He figures that his pension will start at about $60,000 and it will have the same 3% annual increase. He wants to know which plan will pay out the largest total by age 80. Show him how to determine the answer to his question. Homework Help ✎

Find the sum of the geometric series defined by *t*(*n*) = 30000(1.03)^{n}^{ − 1} from 1 to 25

and the sum of the geometric series defined by *t*(*n*) = 60000(1.03)^{n}^{ − 1} from 1 to 15.