1 2 pts You plan for college for your new baby so you start

1) (2 pts) You plan for college for your new baby, so you start investing money into an account as soon as he is born (time t-0.....through t-17). You anticipate withdrawing $20,000 each year for 4 years when the child is 18, 19, 20, and 21 years old. After the last withdraw, the account will have a balance of zero. How much will you need to invest each year if the interest rate on the account is constant for the life of the account at 5% compounded annually?

Solution

We cannot withdraw more than what we have when the child is 17 years old. We invest X now and then X each year till 17 years. If we invest $X each year, for 17 yeras, at 5 percent rate of interest compounded annually, we would have an amount at the end of 17 years equal to

V₁₇ = X + X (F/A, 5%, 17) = X + X * 25.8404. Hence we have 26.8404X after 17 years. This is the amount that we can withdraw in next four years. Hence we need to find \'X\' so that we have

20000 = (26.8404X)*(A/P, 5%, 4)

20000 = 26.8404*0.2820X

This gives X = 2,642.35

You must invest $2,642.35 each year for 17 years to withdraw $20000 each year thereafter for four years.