CHAPTER 5 LESSON 5 Exponential Functions and Investing

Compound Annual Interest

Future Value of an Account

Future Value of an Investment with Periodic Compounding

Daily Versus Annual Compounding of Interest  Write the equation that gives the future value of $1000 invested for t years at 8% compounded annually.  Write the equation that gives the future value of $1000 invested for t years at 8% compounded daily.  Graph the equations from the parts above on the same axes with t between 0 and 30.  What is the additional amount of interest earned in 30 years from compounding daily rather than annually.

Number e

Type of Compounding Number of Compounding Periods per Year Future Value in $ Annually1 Quarterly4 Monthly12 Daily365 Hourly8760 Each Minute525,600 X times per yearX

Number e  As the table indicates, the future value increases (but not very rapidly) as the number of compounding periods during the year increases.  As x gets very large, the future value approaches the number e

Compounding Continuously

Future Value and Continuous Compounding  What is the future value of $2650 invested for 8 years at 12% compounded continuously?  How much Interest will be earned on this investment?

Continuous Versus Annual Compounding of Interest  For each of 9 years, compare the future value of an investment of $1000 at 8% compounded both annually and continuously.  Graph the functions for annual and continuous compounding for t = 30 years on the same axes.  What conclusion can be made regarding compounding annually and compounding continuously?

Present Value of an Investment

Present Value  What lump sum must be invested at 10% compounded semiannually for the investment to grow to $15,000 in 7 years?

Mutual Fund Growth  The data in the table give the annual return on an investment of $1.00 made on March 31,1990, in the AIM Value Fund, Class A Shares. The values reflect reinvestment of all distributions and changes in net asset value but exclude sales charges.  Use an exponential function to model this data.  Use the model to find what the fund will amount to on March 31, 2001 if $10000 is invested March 31, 1990 and the fund continues to follow this model after  Is it likely that this fund continued to grow at this rate in 2002? Time (years) Avg. Annual Total Return ($)

Homework  Pages  1-7,13-15,17, 19,21,23-29,36