Mizzy Elliott plans to pay her daughter’s tuition for four years starting eighteen (18) years from...

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?

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Expert Solution

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.

jeff jeffy answered 11 months ago

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