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Worksheet on Future and Present Value using Exponential Functions, Assignments of Mathematics

University of South Carolina (USC) - ColumbiaMathematics

This worksheet from january 27, 2006, covers the concepts of future and present value of money using exponential functions. It includes problem-solving exercises to calculate the value of investments with different growth rates and time periods. Students are expected to use their calculators and fill in a chart with given values.

Typology: Assignments

Pre 2010

Uploaded on 10/01/2009

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koofers-user-6kq-1 🇺🇸

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Worksheet #5 - Future and Present Value
January 27, 2006
Remember some of the rules for using exponentials.
ln(A·B) = ln(A) + ln(B)
ln(Ap) = p·ln(A)
Problem #1:
•Use your calculator to fill in the chart. Use four-decimal places in your
calculations.
x ln(x)
1
2
3
5
10
15
30
•What is the value of ln(2) + ln(5) ? Is it ln(7) ?
•What is the value of ln(2) + ln(3) + ln(5) ? Is it ln(10) ?
•What is the value of ln(30) −ln(2) ? Is it ln(28) ?
pf2

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Worksheet #5 - Future and Present Value

January 27, 2006

Remember some of the rules for using exponentials.

ln(A · B) = ln(A) + ln(B)

ln(Ap) = p · ln(A)

Problem #1:

  • Use your calculator to fill in the chart. Use four-decimal places in your calculations.

x ln(x) 1 2 3 5 10 15 30

  • What is the value of ln(2) + ln(5)? Is it ln(7)?
  • What is the value of ln(2) + ln(3) + ln(5)? Is it ln(10)?
  • What is the value of ln(30) − ln(2)? Is it ln(28)?

Worksheet #5 - Future and Present Value

January 27, 2006

Future and Present Value of Money is an important application of exponential functions. Know how to build a table to keep the different values and years or- ganized when doing these problems. The basic formulas that you will be using are:

F = P (1 + r)t F = P · ert Problem #2:

  • How much is $300 worth in 10 years if it can grow at 5.5% per year?
  • How much is $300 in 10 years worth today if it can grow at 5.5% per year?
  • How much is $8000 in 20 years if it can grow at 6.25% per year? How much is $8000 in 20 years if it can grow at a continuous annual rate of 6.25%?
  • If the growth rate of money is 4% annually, how much is receiving three separate payments of $500 after 5 years, after 10 years, and after 15 years worth in today’s dollars?
  • If the growth rate of money is 4% annually, how much is receiving three separate payments of $500 in 8 years, $1000 in 10 years, and $1500 in 12 years worth in today’s dollars?