Question

Mizzy Elliott plans to pay her daughter’s tuition for four years starting eighteen (18) years from now. The current annual cost of college is $7,500 and she expects this cost to rise at an annual rate of 5 percent. She assumes that she can earn 6 percent annually in her planning. How much must Missy put aside each year, starting next year, if she plans to make 17 equal payments?

Answer 1

Annual cost of college fees in 18^th year = $ 7,500 x (1+0.05)¹⁸ = $ 7,500 x (1.05)¹⁸

                                                               = $ 7,500 x 2.40661923369108 = $ 18,049.64

Annual cost of college fees in 19^th year = $ 7,500 x (1+0.05)¹⁹ = $ 7,500 x (1.05)¹⁹

                                                               = $ 7,500 x 2.52695019537564 = $ 18,952.13

Annual cost of college fees in 20^th year = $ 7,500 x (1+0.05)²⁰ = $ 7,500 x (1.05)²⁰

                                                               = $ 7,500 x 2.65329770514442 = $ 19,899.73

Annual cost of college fees in 21^th year = $ 7,500 x (1+0.05)²¹ = $ 7,500 x (1.05)²¹

                                                               = $ 7,500 x 2.78596259040164 = $ 20,894.72

Total value of college fees in year 17 = $ 18,049.64/ (1+0.06) + $ 18,952.13/ (1+0.06)² + $ 19,899.73 (1+0.06)³ + $ 20,894.72 / (1+0.06)⁴

= $ 18,049.64/ (1.06) + $ 18,952.13/ (1.06)² + $ 19,899.73/ (1.06)³ + $ 20,894.72 / (1.06)⁴

= $ 18,049.64/1.06 + $ 18,952.13/ 1.1236 + $ 19,899.73/1.191016+ $ 20,894.72 / 1.26247696

= $ 17,027.9622641509 + $ 16,867.3282306871 + $ 16,708.1970351364 + $ 16,550.5753071327

= $ 67,154.0628371071 or $ 67,154.06

Future value of 17 equal deposits should be $ 67,154.06 which can be computed using formula for FV of annuity as:

FV = P x [(1+r) ⁿ – 1/r]

P = FV/ [(1+r) ⁿ – 1/r]

P = Periodic deposit

r = Rate per period = 6 %

n = Numbers of periods = 17

P = $ 67,154.06/ [(1+0.06) ¹⁷ – 1/0.06]

   = $ 67,154.06/ [(1.06) ¹⁷ – 1/0.06]

   = $ 67,154.06/ [(2.69277278576681– 1)/0.06]

= $ 67,154.06/ (1.69277278576681/0.06)

   = $ 67,154.06/ 28.2128797627802

= $ 2,380.26251005375 or $ 2,380.26

Missy must put aside $ 2,380.26 for daughter’s college fees.