### Home > CCA2 > Chapter Ch10 > Lesson 10.2.1 > Problem10-96

10-96.

Joe's dad is only $40$, but he's already thinking about retiring. If he retires early at age $55$, he will receive an annual pension starting at $30{,}000$ and increasing at a rate of $3\%$ each year to account for inflation. If he waits until he is $65$, his pension will be a larger percentage of his salary at that time. He figures that it will be about $60{,}000$ to start and the same $3\%$ increase after that for inflation. He wants to know which plan will pay out the largest total by age $80$. Show him how to find out the answer to his question.

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 $15$.