Question

Joe and Sarah Fabozzi are saving for the college education of their 1 year old daughter, Beth. The Fabozzi's estimate that college expenses will run $35,000 pear year when their daughter reaches college in 17 years. In other words, the first withdrawal will be made on Beth's 18th Birthday and the last payment will be made on Beth's 17th Birthday. The expected interest rate while saving and in college is 6%. Assume today is Beth's first birthday and the first deposit will be made one year from today. Calculate the annual payment the Fabozzi's must make to the account so that their daughter will be completely supported through four years of college. (Enter a positive value and round to 2 decimals)

Answer 1

Solving this question is a 2 step process:

In the first step we calculate the total value of savings as on her 18th birthday. This can be done using the Present Value (PV) function in Excel or any financial calculator.

Manually also it can be done by using the PVIFA table & looking up the factor for 6% interest rate column & 4 years row. The factor is 3.465. Then multiply the factor with 35,000 to get the same (approx.) result as above.

i.e. PV= PVIFA(4 years, 6%) * 35,000

The Excel screenshot is shown below along with the formula:

6% Interest rate College expense per year 35000 Number of years of college On 18th birthday, the PV of next 4 years expenses will be =PV(6%,4,-35000) $ 1,21,278.70

In the next part, we treat this value as the future value of the annual savings of the parents. Note that they will start the savings from the next year, i.e. Beth's 2nd birthday & last payment will be on 17th birthday. So there will be 16 annual payments.

The calculation for the required annual savings in Excel is shown below (On a financial calculator also you can use the same PMT function with given inputs):

Present Value Number of years of savings Future value Required Annual payment 16 1,21,278.70 -4,724.07 =PMT(6%, 16,0,121278.70) $

So they must save $4,724.07 annually for this purpose

( If you need to calculate using tables, then lookup the FVIFA table for 16 years row & 6% column. The factor is 25.673. Divide the future value by this factor to get the same answer. )

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