19. Beth has just had her 45th birthday. She has two children. One will go to co

Question

19. Beth has just had her 45th birthday. She has two children. One will go to college 4 years from now and require four year beginning-of-year payments for college expenses, $18,000, $19,500, $20,500, and $21,500. The other will go to college 9 years from now and require four year beginning-of-year payments for college expenses, $23,000, $23,500, $24,000, and $24,500. In addition, Beth plans to retire in 20 years. Beth wants to be able to withdraw $100,000 per year (at the end of each year) from an account for 25years. The first withdraw occurs on her 66st birthday. What equal, annual, end –of-year amount must Beth save for each of the next 20 years to meet these goals if all savings earn a 8% annual rate of return?

A. $118,997.63

B. $30,296.10

C. $32,939.42

D. $133,725.15

Explanation / Answer

First we will calculate the net present value of all required expenses.

NPV = 18000(1.08)-4+19500(1.08)-5+20500(1.08)-6+21500(1.08)-7+23000(1.08)-9+23500(1.08)-10+24000(1.08)-11+24500(1.08)-12+100000(1-1.08-25) x 1.08-20/0.08

NPV = 308476.32

The yearly payment P each year should be:

308476.32 = P(1-1.08-20) / .08

P=$31418.99

The answer must be 30296.1 yearly .(B) Pls check calculation once

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