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.