Question

Time Value of Money Problem

(This problem was originally written many years ago, when it was true. It represents a valid application of the principles of Time Value of Money.)

I have two children, ages 5 and 7. If I wish to put money away beginning this year to pay for their college education, I need to identify the amount that I must save each year.

Child 1 will go to college in 11 years.

Child 2 will go to college in 13 years.

The annual interest rate will be 10 per cent and will be compounded annually.

I will need $25,000 per child per year of college for four years of college for each child.

How much must I put away each year beginning at the end of this year?

Part 1. Compute the annual payment to be made each year so that I will have exactly covered the required amounts when the second child completes the fourth year of college. As a simplifying assumption, we will assume that the college will allow a single tuition payment to be made at the end of each year. I want to put away the same amount every year until the obligation is completed.

Show the steps taken to solve the problem and explain why these steps are taken.

Part 2. Assume I was smarter and began the savings process when my second son was born. That is, five years earlier than the first part of this problem. What would the payments have been if I began five years earlier?

Part 3. Identify one or more reasonable investment opportunities that will permit me to earn 10 percent on my money. Explain why the identified in vestment choice is appropriate. Your investment choice must reasonably permit the addition or withdrawal of funds as appropriate throughout the term of the problem.

Answer 1

1.

$25000 will have to be paid at the end of 12,13,14 and 15 years for 1st child and

$25000 will have to be paid at the end of 14,15,16 and 17 years for 2nd child   

So, present value of cost

= (25000/1.1^12+25000/1.1^13+25000/1.1^14+25000/1.1^15)+(25000/1.1^14+25000/1.1^15+25000/1.1^16+25000/1.1^17)

=$50730.39

The present value of savings ($A each year) starting at the end of 1st year till the end of year 17

=A/1.1 +A/1.1^2+....+A/1.1^17

=A/0.1*(1-1/1.1^17)

=A*8.021553

To exactly match the savings with the expenditure, the present values must match

A*8.021553 = 50730.39

=> A = $6324.26

So, $6324.26 must be put away every year starting at the end of year for 17 years to fund the education of the two children

2. If savings started 5 years ago and continued till the end of education (22 years), I would have accumulated some amount by today = A/0.1*(1.1^5-1) = 6.1051*A

and hence

A*8.021553+ A*6.1051 = 50730.39

=> A =$3591.11

The payments would have been only $3591.11 had I started 5 years earlier

3. The Equity market or the Mutual Funds market provides a reasonable investment opportunities where one can earn 10% or more. As the investment is for a long duration , investment in these markets may be done (for short duration, these markets are risky)