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# Analysis: Time Value of Money Scenarios

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1. Dr. I. N. Stein has just invested \$6,250 for his son (age one). The money will be used for his son's education 17 years from now. He calculates that he will need \$50,000 for his son's education by the time the boy goes to school. What rate of
return will Dr. Stein need to achieve this goal?

2. Betty Bronson has just retired after 25 years with the electric company. Her total pension funds have an accumulated value of \$180,000, and her life expectancy is 15 more years. Her pension fund manager assumes he can earn a 9 percent return on her assets. What will be her yearly annuity for the next 15 years?

3. Larry Davis borrows \$80,000 at 14 percent interest toward the purchase of a home. His mortgage is for 25 years.
a. How much will his annual payments be? (Although home payments are usually on a monthly basis, we shall do our analysis on an annual basis for ease of computation. We will get a reasonably accurate answer.)
b. How much interest will he pay over the life of the loan?
c. How much should he be willing to pay to get out of a 14 percent mortgage and into a 10 percent mortgage with 25 years remaining on the mortgage? Assume current interest rates are 10 percent. Carefully consider the time value of money. Disregard taxes.

4. Sue Sussman started a paper route on January 1, 1998. Every three months, she deposits \$500 in her bank account, which earns 4 percent annually but is compounded quarterly. On December 31, 2001, she used the entire balance in her bank account to invest in a contract that pays 9 percent annually. How much will she have on December 31, 2004?

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#### Solution Preview

Note: For the following answers the abbreviations have the following meanings

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

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

Dr. I. N. Stein has just invested \$6,250 for his son (age one). The money will be used for his son's education 17 years from now. He calculates that he will need \$50,000 for his son's education by the time the boy goes to school. What rate of return will Dr. Stein need to achieve this goal?

Future Value : Amount at the end of 17 years= \$50,000
Present Value V: Amount invested now= \$6,250

Future Value = Present Value x FVIF
or FVIF = 8.00 =\$50,000 / \$6,250

FVIF (17 years, r%)= 8.00
Looking up in the tables r= 13.00%

n= 17
r= 13.00%
FVIF (17 periods, 13.% rate ) = 7.9861

Answer: Return Dr. Stein needs to achieve this goal = 13.00%

Betty Bronson has just retired after 25 years with the electric company. Her total pension funds have an accumulated value of \$180,000, and her life expectancy is 15 more years. Her pension fund manager assumes he can earn a 9 percent return on her assets. What will be her yearly annuity for the next 15 years?

Present Value= \$180,000
Present Value = ...

#### Solution Summary

In an attached Excel spreadsheet, this solution responds to the 4 time value of money scenarios, calculating the rates of return, yearly annuity and future value. By clicking directly onto the cells of the spreadsheet, this solution illustrates what calculations are required to derive the desired values.

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