Question

Your younger sister, Jennifer, will start college in five years. She has just informed your parents that she wants to go to Eastern State U., which will cost $20,000 per year for four years (cost assumed to come at the end of each year). Anticipating Jennifer's ambitions, your parents started investing $3,000 per year five years ago and will continue to do so for five more years. How much more will your parents have to invest each year for the next five years to have the necessary funds for Jennifer's education? Use 10% as the appropriate interest rate throughout this problem.

(please demonstrate clear formulas thanks)

Answer 1

Value of college cost at the end of 5th year from now = 20,000*PVIFA(10%,4)

= 20,000*3.1699

= $63,398

.

.

Present Value of investments made by Parents for last 5 years = 3,000*FVIFA(10%,5)

= 3,000*6.1051

= $18,315.30

.

Future Value of the above investment after 5 years from now = 18,315.30*(1.10^5)

= $29,496.97

.

Balance Future Value required to fund the college fees cost of Jennifer = $63,398 - $29,496.97

= $33,901.03

.

Let the amount to be invested by parents each year for the next five years to have the necessary funds for Jennifer's education be $x

,

Future value of such amount should be equal to $33,901.03

.

Therefore,

x*FVIFA(10%,5) = 33,901.03

x*6.1051 = 33,901.03

x = 33,901.03/6.1051

x = 5,552.90

.

.

So , parents have to invest $5,552.90 each year for the next five years to have the necessary funds for Jennifer's education.