example 2 daily versus annual compounding of interest chapter 5.5 a.write the equation that gives...
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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
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?
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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