You are saving for the college education of your two children. They are two year

Question

You are saving for the college education of your two children. They are two years apart in age; one will begin college 15 years from today and the other will begin 17 years from today. You estimate your children’s college expenses to be $47,000 per year per child, payable at the beginning of each school year. The annual interest rate is 8.1 percent. Your deposits begin one year from today. You will make your last deposit when your oldest child enters college. Assume your children will be on the four-year plan. How much money must you deposit in an account each year to fund your children’s education? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Annual savings

Explanation / Answer

College Expenses:
Year 15 = $47,000
Year 16 = $47,000
Year 17 = $47,000 + $47,000 = $94,000
Year 18 = $47,000 + $47,000 = $94,000
Year 19 = $47,000
Year 20 = $47,000

Annual Interest Rate = 8.10%

Present Value of College Expenses = $47,000/1.081^15 + $47,000/1.081^16 + $94,000/1.081^17 + $94,000/1.081^18 + $47,000/1.081^19 + $47,000/1.081^20
Present Value of College Expenses = $96,872.24

Present Value of Annual Deposit = $96,872.24
Annual Deposit * PVIFA (8.10%, 15) = $96,872.24
Annual Deposit * (1 - (1/1.081)^15) / 0.081 = $96,872.24
Annual Deposit * 8.50746 = $96,872.24
Annual Deposit = $11,386.74

So, annual saving is $11,386.74

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