example 2 daily versus annual compounding of interest chapter 5.5 a.write the equation that gives...
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![Page 1: Example 2 Daily Versus Annual Compounding of Interest Chapter 5.5 a.Write the equation that gives the future value of $1000 invested for t years at 8%](https://reader035.vdocuments.us/reader035/viewer/2022062409/5697bf891a28abf838c8a14c/html5/thumbnails/1.jpg)
example 2 Daily Versus Annual Compounding of Interest
Chapter 5.5
a. Write the equation that gives the future value of $1000 invested for t years at 8% compounded annually.
b. Write the equation that gives the future value of $1000 invested for t years at 8% compounded daily.
c. Graph the equations from parts (a) and (b) on the same axes with t between 0 and 30.
d. What is the additional amount of interest earned in 30 years from compounding daily rather than annually?
2009 PBLPathways
![Page 2: Example 2 Daily Versus Annual Compounding of Interest Chapter 5.5 a.Write the equation that gives the future value of $1000 invested for t years at 8%](https://reader035.vdocuments.us/reader035/viewer/2022062409/5697bf891a28abf838c8a14c/html5/thumbnails/2.jpg)
2009 PBLPathways
a. Write the equation that gives the future value of $1000 invested for t years at 8% compounded annually.
b. Write the equation that gives the future value of $1000 invested for t years at 8% compounded daily.
c. Graph the equations from parts (a) and (b) on the same axes with t between 0 and 30.
d. What is the additional amount of interest earned in 30 years from compounding daily rather than annually?
![Page 3: Example 2 Daily Versus Annual Compounding of Interest Chapter 5.5 a.Write the equation that gives the future value of $1000 invested for t years at 8%](https://reader035.vdocuments.us/reader035/viewer/2022062409/5697bf891a28abf838c8a14c/html5/thumbnails/3.jpg)
2009 PBLPathways
a. Write the equation that gives the future value of $1000 invested for t years at 8% compounded annually.
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
1 dollarsk t
rS P
k
rk
$1000
0.08
1
P
r
k
1000 1 0.08
1000 1.08
t
t
S
![Page 4: Example 2 Daily Versus Annual Compounding of Interest Chapter 5.5 a.Write the equation that gives the future value of $1000 invested for t years at 8%](https://reader035.vdocuments.us/reader035/viewer/2022062409/5697bf891a28abf838c8a14c/html5/thumbnails/4.jpg)
2009 PBLPathways
a. Write the equation that gives the future value of $1000 invested for t years at 8% compounded annually.
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
1 dollarsk t
rS P
k
rk
$1000
0.08
1
P
r
k
1000 1 0.08
1000 1.08
t
t
S
![Page 5: Example 2 Daily Versus Annual Compounding of Interest Chapter 5.5 a.Write the equation that gives the future value of $1000 invested for t years at 8%](https://reader035.vdocuments.us/reader035/viewer/2022062409/5697bf891a28abf838c8a14c/html5/thumbnails/5.jpg)
2009 PBLPathways
a. Write the equation that gives the future value of $1000 invested for t years at 8% compounded annually.
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
1 dollarsk t
rS P
k
rk
$1000
0.08
1
P
r
k
1000 1 0.08
1000 1.08
t
t
S
![Page 6: Example 2 Daily Versus Annual Compounding of Interest Chapter 5.5 a.Write the equation that gives the future value of $1000 invested for t years at 8%](https://reader035.vdocuments.us/reader035/viewer/2022062409/5697bf891a28abf838c8a14c/html5/thumbnails/6.jpg)
2009 PBLPathways
a. Write the equation that gives the future value of $1000 invested for t years at 8% compounded annually.
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
1 dollarsk t
rS P
k
rk
$1000
0.08
1
P
r
k
1000 1 0.08
1000 1.08
t
t
S
![Page 7: Example 2 Daily Versus Annual Compounding of Interest Chapter 5.5 a.Write the equation that gives the future value of $1000 invested for t years at 8%](https://reader035.vdocuments.us/reader035/viewer/2022062409/5697bf891a28abf838c8a14c/html5/thumbnails/7.jpg)
2009 PBLPathways
a. Write the equation that gives the future value of $1000 invested for t years at 8% compounded annually.
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
1 dollarsk t
rS P
k
rk
$1000
0.08
1
P
r
k
1000 1 0.08
1000 1.08
t
t
S
![Page 8: Example 2 Daily Versus Annual Compounding of Interest Chapter 5.5 a.Write the equation that gives the future value of $1000 invested for t years at 8%](https://reader035.vdocuments.us/reader035/viewer/2022062409/5697bf891a28abf838c8a14c/html5/thumbnails/8.jpg)
2009 PBLPathways
a. Write the equation that gives the future value of $1000 invested for t years at 8% compounded annually.
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
1 dollarsk t
rS P
k
rk
$1000
0.08
1
P
r
k
1000 1 0.08
1000 1.08
t
t
S
![Page 9: Example 2 Daily Versus Annual Compounding of Interest Chapter 5.5 a.Write the equation that gives the future value of $1000 invested for t years at 8%](https://reader035.vdocuments.us/reader035/viewer/2022062409/5697bf891a28abf838c8a14c/html5/thumbnails/9.jpg)
2009 PBLPathways
b. Write the equation that gives the future value of $1000 invested for t years at 8% compounded daily.
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
1 dollarsk t
rS P
k
rk
$1000
0.08
365
P
r
k
3650.08
1000 1365
t
S
![Page 10: Example 2 Daily Versus Annual Compounding of Interest Chapter 5.5 a.Write the equation that gives the future value of $1000 invested for t years at 8%](https://reader035.vdocuments.us/reader035/viewer/2022062409/5697bf891a28abf838c8a14c/html5/thumbnails/10.jpg)
2009 PBLPathways
b. Write the equation that gives the future value of $1000 invested for t years at 8% compounded daily.
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
1 dollarsk t
rS P
k
rk
$1000
0.08
365
P
r
k
3650.08
1000 1365
t
S
![Page 11: Example 2 Daily Versus Annual Compounding of Interest Chapter 5.5 a.Write the equation that gives the future value of $1000 invested for t years at 8%](https://reader035.vdocuments.us/reader035/viewer/2022062409/5697bf891a28abf838c8a14c/html5/thumbnails/11.jpg)
2009 PBLPathways
b. Write the equation that gives the future value of $1000 invested for t years at 8% compounded daily.
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
1 dollarsk t
rS P
k
rk
$1000
0.08
365
P
r
k
3650.08
1000 1365
t
S
![Page 12: Example 2 Daily Versus Annual Compounding of Interest Chapter 5.5 a.Write the equation that gives the future value of $1000 invested for t years at 8%](https://reader035.vdocuments.us/reader035/viewer/2022062409/5697bf891a28abf838c8a14c/html5/thumbnails/12.jpg)
2009 PBLPathways
b. Write the equation that gives the future value of $1000 invested for t years at 8% compounded daily.
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
1 dollarsk t
rS P
k
rk
$1000
0.08
365
P
r
k
3650.08
1000 1365
t
S
![Page 13: Example 2 Daily Versus Annual Compounding of Interest Chapter 5.5 a.Write the equation that gives the future value of $1000 invested for t years at 8%](https://reader035.vdocuments.us/reader035/viewer/2022062409/5697bf891a28abf838c8a14c/html5/thumbnails/13.jpg)
2009 PBLPathways
c. Graph the equations from parts (a) and (b) on the same axes with t between 0 and 30.
30
1000 1.08
1000 1.08
10,062.66
tS
S
365
365 30
0.081000 1
365
0.081000 1
365
11,020.28
t
S
S
Compounded annually
Compounded daily
![Page 14: Example 2 Daily Versus Annual Compounding of Interest Chapter 5.5 a.Write the equation that gives the future value of $1000 invested for t years at 8%](https://reader035.vdocuments.us/reader035/viewer/2022062409/5697bf891a28abf838c8a14c/html5/thumbnails/14.jpg)
2009 PBLPathways
c. Graph the equations from parts (a) and (b) on the same axes with t between 0 and 30.
30
1000 1.08
1000 1.08
10,062.66
tS
S
365
365 30
0.081000 1
365
0.081000 1
365
11,020.28
t
S
S
Compounded annually
Compounded daily
t
S
![Page 15: Example 2 Daily Versus Annual Compounding of Interest Chapter 5.5 a.Write the equation that gives the future value of $1000 invested for t years at 8%](https://reader035.vdocuments.us/reader035/viewer/2022062409/5697bf891a28abf838c8a14c/html5/thumbnails/15.jpg)
2009 PBLPathways
30
1000 1.08
1000 1.08
10,062.66
tS
S
365
365 30
0.081000 1
365
0.081000 1
365
11,020.28
t
S
S
Compounded annually
Compounded daily
d. What is the additional amount of interest earned in 30 years from compounding daily rather than annually?
t
S
![Page 16: Example 2 Daily Versus Annual Compounding of Interest Chapter 5.5 a.Write the equation that gives the future value of $1000 invested for t years at 8%](https://reader035.vdocuments.us/reader035/viewer/2022062409/5697bf891a28abf838c8a14c/html5/thumbnails/16.jpg)
2009 PBLPathways
30
1000 1.08
1000 1.08
10,062.66
tS
S
365
365 30
0.081000 1
365
0.081000 1
365
11,020.28
t
S
S
Compounded annually
Compounded daily
d. What is the additional amount of interest earned in 30 years from compounding daily rather than annually?
t
S
![Page 17: Example 2 Daily Versus Annual Compounding of Interest Chapter 5.5 a.Write the equation that gives the future value of $1000 invested for t years at 8%](https://reader035.vdocuments.us/reader035/viewer/2022062409/5697bf891a28abf838c8a14c/html5/thumbnails/17.jpg)
2009 PBLPathways
30
1000 1.08
1000 1.08
10,062.66
tS
S
365
365 30
0.081000 1
365
0.081000 1
365
11,020.28
t
S
S
Compounded annually
Compounded daily
d. What is the additional amount of interest earned in 30 years from compounding daily rather than annually?
t
S
![Page 18: Example 2 Daily Versus Annual Compounding of Interest Chapter 5.5 a.Write the equation that gives the future value of $1000 invested for t years at 8%](https://reader035.vdocuments.us/reader035/viewer/2022062409/5697bf891a28abf838c8a14c/html5/thumbnails/18.jpg)
2009 PBLPathways
30
1000 1.08
1000 1.08
10,062.66
tS
S
365
365 30
0.081000 1
365
0.081000 1
365
11,020.28
t
S
S
Compounded annually
Compounded daily
d. What is the additional amount of interest earned in 30 years from compounding daily rather than annually?
t
S
![Page 19: Example 2 Daily Versus Annual Compounding of Interest Chapter 5.5 a.Write the equation that gives the future value of $1000 invested for t years at 8%](https://reader035.vdocuments.us/reader035/viewer/2022062409/5697bf891a28abf838c8a14c/html5/thumbnails/19.jpg)
2009 PBLPathways
30
1000 1.08
1000 1.08
10,062.66
tS
S
365
365 30
0.081000 1
365
0.081000 1
365
11,020.28
t
S
S
Compounded annually
Compounded daily
d. What is the additional amount of interest earned in 30 years from compounding daily rather than annually?
t
S
![Page 20: Example 2 Daily Versus Annual Compounding of Interest Chapter 5.5 a.Write the equation that gives the future value of $1000 invested for t years at 8%](https://reader035.vdocuments.us/reader035/viewer/2022062409/5697bf891a28abf838c8a14c/html5/thumbnails/20.jpg)
2009 PBLPathways
30
1000 1.08
1000 1.08
10,062.66
tS
S
365
365 30
0.081000 1
365
0.081000 1
365
11,020.28
t
S
S
Compounded annually
Compounded daily
d. What is the additional amount of interest earned in 30 years from compounding daily rather than annually?
t
S
$11,020.28 $10,062.66 $957.62