Question

Jimmy is starting Grade 2 tomorrow (assume September 1st). Jimmy’s parents anticipate that after graduation from high school (i.e., completion of Grade 12), he will attend university and major in finance. They expect that the annual, all-inclusive cost of university will be $20,000, to be incurred at the beginning of each year. Jimmy’s parents expect it to take him a total of six years to complete both a BBA and an MBA degree and they would like to fully finance his university education.

In order to do so, they intend to invest a fixed amount annually each August 31st starting next year until Jimmy is ready to begin university, at which point they wish to have exactly enough money saved to pay for his education. Assume that the annual interest rate will remain at 10% until Jimmy starts university and that it will be 8% thereafter. Assume Jimmy completes his schooling without repeating any courses or grades. Assume no income taxes apply. How much money should Jimmy’s parents invest each year so that his university education is exactly financed?

Answer 1

Compute the PVIFA at 8% and 5 years, using the equation as shown below:

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

                   = {1 – (1 + 0.08)^-5}/ 8%

            = 3.99271

Hence, the PVIFA at 8% and 5 years is 3.99271.

Compute the value of annuity after 10 years, using the equation as shown below:

Annuity value = Annual college expenses*(1 + PVIFA_{8%, 5 years})

                       = $20,000*(1 + 3.99271)

                       = $87,985.42

Hence, the annuity value after 10 years is $87,985.42.

Compute the PVIFA at 10% and 10 years, using the equation as shown below:

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

                   = {1 – (1 + 0.10)^-10}/ 10%

            = 6.144567

Hence, the PVIFA at 10% and 10 years is 6.144567.

Compute the PVIF at 10% and 10 years, using the equation as shown below:

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

              = 1/ (1 + 0.10)¹⁰

         = 1/ 2.5937

         = 0.385543

Hence, the PVIF at 10% and 10 years is 0.385543.

Compute the annual investment, using the equation as shown below:

Annual investment = Annuity after 10 years*PVIF_{10%, 10 years}/ PVIFA_{10%, 10 years}

                              = $87,985.42*0.385543/ 6.144567

                               = $5,520.6759

Hence, the annual investment is $5,520.6759.