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# Time Value of Money Problems

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1. Future value: Chuck Tomkovick is planning to invest \$25,000 today in a mutual fund that will provide a return of 8 percent each year. What will be the value of the investment in 10 years?

2. Patrick Seeley has \$2,400 that he is looking to invest. His brother approached him with an investment opportunity that could double his money in four years. What interest rate would the investment have to yield in order for Patrick's brother to deliver on his promise?

3. Growing perpetuity: You are evaluating a growing perpetuity product from a large financial services firm. The product promises an initial payment of \$20,000 at the end of this year and subsequent payments that will thereafter grow at a rate of 3.4 percent annually. If you use a 9 percent discount rate for investment products, what is the present value of this growing perpetuity?

4. Computing annuity payment: Gary Whitmore is a high school sophomore. He currently has \$7,500 in a money market account paying 5.65 percent annually. He plans to use this and his savings over the next four years to buy a car at the end of his sophomore year in college. He estimates that the car will cost him \$12,000 in four years. How much should he invest in the money market account every year for the next four years if he wants to achieve his target?

#### Solution Preview

Solution:

Problem : 1

Present Value =PV=\$25000
r=rate of return=8%
n=time period=10 years
FV=PV*(1+r/100)^n=25000*(1+8/100)^10=\$53973.12

Problem : 2

PV=\$2400
FV=2*2400=\$4800
n=4 years
We know ...

#### Solution Summary

There are 4 problems. Solution to first problem explains the formula to calculate future value of an investment. Solution to second problem calculates the needed interest rate. Solution to third problem depicts the formula to calculate present value of growing perpetuity. Solution to last problem explains the methodology to calculate the annuity payment.

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