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# Appications of Time Value of Money Concepts

1. Assuming that the current interest rate is 3 percent, compute the value of a three year, 5 percent coupon bond with a face value of \$1,000. What happens when the interest rate goes to 4 percent? What happens when the interest rate goes to 2 percent?

2. Some friends of yours have just had a child. Thinking ahead, and realizing the power of compound interest, they are considering investing for their child's college education, which will begin in 18 years. Assume that the cost of a college education today is \$150,000; there is no inflation; and there are no taxes on interest income that is used to pay college tuition and expenses.

a. If the interest rate is 5 percent, how much money will your friends need to put into their savings account today to have \$150,000 in 18 years?
b. What if the interest rate were 10% percent?
c. The chance that the price of a college education will be the same 18 years from now as it is today seems remote. As summing that the price will rise 3% per year, and that today's interest rate is 8 percent, what will your friend's investment need to be?
bo
3. You are considering going to graduate school for a one-year master's program. You have done some research and believe that the master's degree will add \$6,000 per year to your salary for the next 10 years of your working life, starting at the end of this year. From then on, after the next 10 years, it makes no difference. Completing the master's program will cost you \$36,000, which you would have to borrow at an interest rate of 6%. Is this investment in your education profitable? Explain your answer.

#### Solution Preview

PROBLEM 1:
Coupon amount=C=1000*5%=\$50
Number of coupons=n=3
Maturity amount=Face Value=M=\$1000
Interest rate=r=3%
Fair Value of bond= C/r*(1-1/(1+r)^n)+M/(1+r)^n
=50/3%*(1-1/(1+3%)^3)+1000/(1+3%)^3=\$1056.57

In case,
Interest rate=r=4%
Fair Value of bond= C/r*(1-1/(1+r)^n)+M/(1+r)^n
...

#### Solution Summary

There are three basic questions related to concepts in time value of money. Solution to first problem depicts the steps to analyze the effect of changes in interest rate on price of a bond. Solution to second problem describes the methodology to calculate the lump sum needed to meet the given financial target of education expanses. Solution to third problem analyzes if it is worth to study further and have a master's degree.

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