Question

Suppose you have a newborn child and want to begin covering the estimated cost of tuition and expenses for four years of college beginning 18 years from now.

Your estimated cost is $42,000 per year beginning at the end of year 18 and running through the end of year 21 (4 years). Assume a nominal interest of 15% compounded annually.

A) What is the value of the payments at the beginning of year 18 (end of year 17)?

B) How much would you have to invest today (time zero) to cover the estimated cost of four years of college?

C) What uniform series of deposits at the end of each of years 1 through 17 would be required to cover the tuition costs in years 18 through 21?

Answer 1

Solution:

a)Calculation of Present value of annual payment of $42,000

Annuity=$42,000

n=4

r=15% or 0.15

Present Value=Annuity*Present value of annuity factor@15% for 4 years

=$42,000*2.85497836268

=$119,909.09

Thus the value of the payments at the beginning of year 18 is $119,909.09

b)Calculation of Present value of $119,909.09

Present Value=Future value/(1+r)^n

=$119,909.09/(1+0.15)^17

=$11,142.66

Thus I have to invest $11,142.66 today.

c)Calculation of Annuity amount

Future Value=Annuity*[(1+r)^n-1)/r]

$11,142.66=Annuity*[1+0.15)^17-1/0.15]

Annuity=$119,909.09/65.075093

=$1842.63