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# Time Value of Money Applied

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1 Your younger sister, Jennifer, will start college in five years. She has just informed your parents that she wants to go to Penn State U,. which will cost \$18,000 per year for four years (cost assumed to come at teh 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 funds for her education? Use 10 percent as the appropriate interest rate throughout the problem (for discounting or compounding).

2. Jennifer (from problem 1) is now 18 years old (five years have passed), and she wants to get married instead of going to college. Your parents have accumulated the necessary funds for her education.
Instead of her schooling, your parents are paying \$7,000 for her current wedding and plan to take year-end vacations costing \$2,000 per year for the next three years.
How much money will your parents have at the end of three years to help you with graduate school, which you will start then? You plan to work on a master's perhaps a Ph.D. If graduate school costs \$18,930 per year, approximately how long will you be able to stay in school based on these funds? Use 10 percent as the appropriate interest rate throughout this problem. (Round all values to whole numbers.)

#### Solution Preview

Note: the abbreviations have the following meanings

PVIF= Present Value Interest Factor
FVIF= Future Value Interest Factor

PVIFA= Present Value Interest Factor for an Annuity
FVIFA= Future Value Interest Factor for an Annuity

They can be read from tables or calculated using the following equations
PVIF( n, r%)= =1/(1+r%)^n
FVIF( n, r%)= =(1+r%)^n

PVIFA( n, r%)= =[1-1/(1+r%)^n]/r%
FVIFA( n, r%)= =[(1+r%)^n -1]/r%

"1 Your younger sister, Jennifer, will start college in five years. She has just informed your parents that she wants to go to Penn State U,. which will cost \$18,000 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 funds for her education? Use 10 percent as the appropriate interest rate throughout the problem (for discounting or compounding). "

First find the present value of college fees for 4 years at the start of college (end of 5 years from now)

n= 4
r= 10.00%
PVIFA (4 periods, 10.% rate ) = 3.169865

Annuity= \$18,000
Therefore, present value= \$57,058 =18,000. x 3.169865

Then find the value today of the \$3,000 that the parents have invested for 5 years

n= 5
r= 10.00%
FVIFA (5 periods, 10.% rate ) ...

#### Solution Summary

Answers Time Value of Money Questions.

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