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.