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Example 4 Continuous Versus Annual Compounding of Interest Chapter 5.5 a.For each of 9 years, compare the future value of an investment of $1000 at 8%

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Presentation on theme: "Example 4 Continuous Versus Annual Compounding of Interest Chapter 5.5 a.For each of 9 years, compare the future value of an investment of $1000 at 8%"— Presentation transcript:

1 example 4 Continuous Versus Annual Compounding of Interest Chapter 5.5 a.For each of 9 years, compare the future value of an investment of $1000 at 8% compounded annually and of $1000 at 8% compounded continuously. b.Graph the functions for annual compounding and for continuous compounding on the same axes. c.What conclusion can be made regarding compounding annually and compounding continuously?  2009 PBLPathways

2 a.For each of 9 years, compare the future value of an investment of $1000 at 8% compounded annually and of $1000 at 8% compounded continuously. b.Graph the functions for annual compounding and for continuous compounding on the same axes. c.What conclusion can be made regarding compounding annually and compounding continuously?

3  2009 PBLPathways a.For each of 9 years, compare the future value of an investment of $1000 at 8% compounded annually and of $1000 at 8% compounded continuously. Future Value of an Investment with Periodic Compounding If $P is invested for t years at the annual interest rate r, where the interest is compounded k times per year, then the interest rate per period is, the number of compounding periods is kt, and the future value that results is given by Compounded annuallyCompounded continuously

4  2009 PBLPathways a.For each of 9 years, compare the future value of an investment of $1000 at 8% compounded annually and of $1000 at 8% compounded continuously. Future Value of an Investment with Periodic Compounding If $P is invested for t years at the annual interest rate r, where the interest is compounded k times per year, then the interest rate per period is, the number of compounding periods is kt, and the future value that results is given by Compounded annuallyCompounded continuously

5  2009 PBLPathways a.For each of 9 years, compare the future value of an investment of $1000 at 8% compounded annually and of $1000 at 8% compounded continuously. Future Value of an Investment with Periodic Compounding If $P is invested for t years at the annual interest rate r, where the interest is compounded k times per year, then the interest rate per period is, the number of compounding periods is kt, and the future value that results is given by Compounded annuallyCompounded continuously

6  2009 PBLPathways a.For each of 9 years, compare the future value of an investment of $1000 at 8% compounded annually and of $1000 at 8% compounded continuously. Future Value of an Investment with Periodic Compounding If $P is invested for t years at the annual interest rate r, where the interest is compounded k times per year, then the interest rate per period is, the number of compounding periods is kt, and the future value that results is given by Compounded annuallyCompounded continuously

7  2009 PBLPathways a.For each of 9 years, compare the future value of an investment of $1000 at 8% compounded annually and of $1000 at 8% compounded continuously. Future Value of an Investment with Continuous Compounding If $P is invested for t years at the annual interest rate r compounded continuously, then the future value S is given by Compounded annuallyCompounded continuously

8  2009 PBLPathways a.For each of 9 years, compare the future value of an investment of $1000 at 8% compounded annually and of $1000 at 8% compounded continuously. Future Value of an Investment with Continuous Compounding If $P is invested for t years at the annual interest rate r compounded continuously, then the future value S is given by Compounded annuallyCompounded continuously

9  2009 PBLPathways a.For each of 9 years, compare the future value of an investment of $1000 at 8% compounded annually and of $1000 at 8% compounded continuously. t 01000.00 11080.001082.29 21166.401173.51 31259.711271.25 41360.491377.13 51469.331491.82 61586.871616.07 71713.821750.67 81850.931896.48 91999.002054.43

10  2009 PBLPathways a.For each of 9 years, compare the future value of an investment of $1000 at 8% compounded annually and of $1000 at 8% compounded continuously. t 01000.00 11080.001083.29 21166.401173.51 31259.711271.25 41360.491377.13 51469.331491.82 61586.871616.07 71713.821750.67 81850.931896.48 91999.002054.43

11  2009 PBLPathways a.For each of 9 years, compare the future value of an investment of $1000 at 8% compounded annually and of $1000 at 8% compounded continuously. t 01000.00 11080.001083.29 21166.401173.51 31259.711271.25 41360.491377.13 51469.331491.82 61586.871616.07 71713.821750.67 81850.931896.48 91999.002054.43

12  2009 PBLPathways a.For each of 9 years, compare the future value of an investment of $1000 at 8% compounded annually and of $1000 at 8% compounded continuously. t 01000.00 11080.001083.29 21166.401173.51 31259.711271.25 41360.491377.13 51469.331491.82 61586.871616.07 71713.821750.67 81850.931896.48 91999.002054.43

13  2009 PBLPathways a.For each of 9 years, compare the future value of an investment of $1000 at 8% compounded annually and of $1000 at 8% compounded continuously. t 01000.00 11080.001083.29 21166.401173.51 31259.711271.25 41360.491377.13 51469.331491.82 61586.871616.07 71713.821750.67 81850.931896.48 91999.002054.43

14  2009 PBLPathways b.Graph the functions for annual compounding and for continuous compounding on the same axes.

15  2009 PBLPathways b.Graph the functions for annual compounding and for continuous compounding on the same axes. t S

16  2009 PBLPathways c.What conclusion can be made regarding compounding annually and compounding continuously? t S

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