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.