### Home > INT3 > Chapter 10 > Lesson 10.2.1 > Problem10-104

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 $15$.