Question

You are currently saving for your child's college education. The current cost of college is $10,000 a year. You expect that college costs will continue to increase at a rate of 5 percent a year. Your child is scheduled to begin attending a four-year college 10 years from now (i.e., college payments will be made at t=10, t=11, t=12, and t=13). You currently have $25,000 in an account which earns 6 percent after taxes. You would like to have all of the necessary savings by the time your child enters college, and you would like to contribute a constant amount at the beginning of each of the next 10 years in order to provide the necessary amount. (You want to make 10 equal contributions starting in Year 0 and ending at Year 9.)

Answer 1

     

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College Fees at the beginning of t = 10

Future Value of College = 10000 * (1+0.05)^10 = 16288.9462675

NOW Present Value of college fees at t = 10

Present Value of Annuity Due with growth =

r = 0.06

G = 0.05

n = 4

=

= 64239.5544677

NOW This will become the future value of Annuity Due from today's perspective.

So.

Future Value of Annuity Due =  

r = 0.06

n = 10

64239.5544677 =

64239.5544677 = Periodic Payment * 13.9716426383

Periodic Payment = 64239.5544677 / 13.9716426383

Periodic Payment = 4597.85

I need to save 4597.85 per year starting from today,