Question

You wish to begin a college education savings program for the benefit of your child, Rebecca, who is 4 years old. Rebecca will begin college at age 18. Currently, the college costs are $10,000 per academic year. You assume that college cost will increase at the rate of 7% annually from now until Rebecca enters college and that you can achieve a before-tax rate of return of 8% annually on funds earmarked for this purpose. They also assume that Rebecca will attend college for 4 years, at which time she will graduate. How much do you have to save monthly for Rebecca’s education?

Answer 1

Compute the annual college expenses, using the equation as shown below:

Annual expenses = Current cost*(1 + Growth rate)^{Number of periods}

                                           = $10,000*(1 + 0.07)^{14 years}

                             = $25,785.3415012

Hence, the annual expenses for college are $25,785.3415012.

Compute the effective annual rate, using the equation as shown below:

Effective annual rate = (1 + Rate of interest/ Compounding period)^{Compounding period} – 1

                                  = (1 + 0.08/ 12)¹² – 1

                                  = 1.083 – 1

                                  = 0.083 or 8.30%

Hence, the effective annual rate is 8.30%.

Compute the PVIFA at 8.30% and 3 years, using the equation as shown below:

PVIFA = {1 – (1 + Rate)^{-Number of periods}}/ Rate

                  = {1 – (1 + 0.083)^-3}/ 8.30%

            = (1 – 0.78725355438)/ 8.30%

            = 2.56321018819

Hence, the PVIFA at 8.30% and 3 years is 2.56321018819.

Compute the value of college expenses after 14 years, using the equation as shown below:

College expenses = Annual expenses*(1 + PVIFA_{8.30%, 3 years})

                             = $25,785.3415012*(1 + 2.56321018819)

                             = $91,878.591543

Hence, college expenses are $91,878.591543.

Compute the monthly interest rate, using the equation as shown below:

Monthly rate = Annual effective rate/ 12 months

                      = 8.30%/12 months

                      = 0.691667%

Hence, the monthly rate of interest is 0.691667%.

Compute the PVIF at 0.691667% and 168 months, using the equation as shown below:

PVIF = 1/ (1 + Rate)^{Number of periods}

              = 1/ (1 + 0.691667%)¹⁶⁸

         = 0.3141

Hence, the PVIF at 0.691667% and 168 months is 0.3141.

Compute the PVIFA at 0.691667% and 168 months, using the equation as shown below:

PVIFA = {1 – (1 + Rate)^{-Number of periods}}/ Rate

                   = {1 – (1 + 0.691667%)^-168}/ 0.691667%

            = (1 – 0.3141)/ 0.691667%

            = 99.1642

Hence, the PVIFA at 0.691667% and 168 months is 99.1642.

Compute the monthly savings for college education, using the equation as shown below:

Monthly savings = College expenses*PVIF_{168 months, 0.691667%}/ PVIFA_{168 months, 0.691667%}

                           = $91,878.591543*0.3141/ 99.1642

                            = $291.023026491

Hence, the monthly savings for college education is $291.023026491.