Question

1. Your child will start college 15 years from today. You believe it will cost $16,000 for the first two years and $18,000 for the last three, payable at the beginning of each year of college. How much do you have to save at the end of each year for 15 years starting now in order to pay tuition and book costs if the account pays 8% interest, compounded annually?

Answer 1

First, we will calculate the present value of college fees paid yearly at the beginning of each at the end of year end 15:

Cash flows for first 2 years = $ 16000

Cash flows for last 3 years = $ 18000

r = Interest rate = 8% compounded annually

Present value = $ 16000 + $14814.81 + $ 15432.10 + $ 14,288.98 + $ 13230.54

So, you should have $ 73766.43 at the end of year 15 to be able to pay for college fees and expenses.

Now, we will calculate the periodic payments each year to be able to generate value at the end of 15 year.

Where, C= Periodic Payments

r = Periodic Interest rate = 0.08

n= no of periods = 15

Present Value = $ 73,766.43

73766.43 = C*8.559478688

C = $ 8618.10

So, $ 8618.10 is to be saved every year for 15 years starting now in order to pay tuition and book costs