Compound Interest and Annuity
13.1 Compound Interest
• Simple interest – interest is paid only on the principal • Compound interest – interest is paid on both principal and interest, compounded at regular intervals • Example: a $1000 principal paying 10% simple interest after 3 years pays .1 3 $1000 = $300
If interest is compounded annually, it pays .1
$1000 = $100 the first year, .1 $1100 = $110 the second year and .1 $1210 = $121 the third year totaling $100 + $110 + $121 = $331 interest
13.1 Compound Interest
Period
Interest
Credited
Times
Credited
per year
Rate per compounding period
Annual
Semiannual
year
1
6 months 2
Quarterly
quarter
4
R
4
Monthly
month
12
R
12
R
R
2
13.1 Compound Interest
• Compound interest formula:
M P (1 i )
n
and
I M P
M = the compound amount or future value
P = principal i = interest rate per period of compounding n = number of periods
I = interest earned
13.1 Compound Interest
• Time Value of Money – with interest of 5% compounded annually.
2000
$1000 $1000
n
(1 i )
(1.05)10
2010
$1000
2020
$1000(1 i ) n
$1000(1.05)10
13.1 Compound Interest
• Example: $800 is invested at 7% for 6 years. Find the simple interest and the interest compounded annually Simple interest:
I PRT $800 .07 6 $336
Compound interest:
M P(1 i ) n $800(1.07)6 $1200.58
I M P $1200.58 $800 $400.58
13.1 Compound Interest
• Example: $32000 is invested at 10% for 2 years. Find the interest compounded yearly, semiannually, quarterly, and monthly yearly: M P(1 i ) n $32000(1.10) 2 $38720
I M P $38720 $32000 $6720 semiannually: M P(1 i ) n $32000(1.05) 4 $38896.20
I M P $38896.20 $32000 $6896.20
13.1 Compound Interest
• Example: (continued) quarterly: M P (1 i ) n $32000(1.025)8 $38988.89
I M P $38988.89 $32000 $6988.89
monthly: i 1012% .833%, n 12 2 24
M P(1 i ) n $32000(1.00833) 24 $39052.20
I M P $39052.20 $32000 $7052.20
13.2 Daily and Continuous
Compounding
• Daily
• Simple interest – interest is paid only on the principal • Compound interest – interest is paid on both principal and interest, compounded at regular intervals • Example: a $1000 principal paying 10% simple interest after 3 years pays .1 3 $1000 = $300
If interest is compounded annually, it pays .1
$1000 = $100 the first year, .1 $1100 = $110 the second year and .1 $1210 = $121 the third year totaling $100 + $110 + $121 = $331 interest
13.1 Compound Interest
Period
Interest
Credited
Times
Credited
per year
Rate per compounding period
Annual
Semiannual
year
1
6 months 2
Quarterly
quarter
4
R
4
Monthly
month
12
R
12
R
R
2
13.1 Compound Interest
• Compound interest formula:
M P (1 i )
n
and
I M P
M = the compound amount or future value
P = principal i = interest rate per period of compounding n = number of periods
I = interest earned
13.1 Compound Interest
• Time Value of Money – with interest of 5% compounded annually.
2000
$1000 $1000
n
(1 i )
(1.05)10
2010
$1000
2020
$1000(1 i ) n
$1000(1.05)10
13.1 Compound Interest
• Example: $800 is invested at 7% for 6 years. Find the simple interest and the interest compounded annually Simple interest:
I PRT $800 .07 6 $336
Compound interest:
M P(1 i ) n $800(1.07)6 $1200.58
I M P $1200.58 $800 $400.58
13.1 Compound Interest
• Example: $32000 is invested at 10% for 2 years. Find the interest compounded yearly, semiannually, quarterly, and monthly yearly: M P(1 i ) n $32000(1.10) 2 $38720
I M P $38720 $32000 $6720 semiannually: M P(1 i ) n $32000(1.05) 4 $38896.20
I M P $38896.20 $32000 $6896.20
13.1 Compound Interest
• Example: (continued) quarterly: M P (1 i ) n $32000(1.025)8 $38988.89
I M P $38988.89 $32000 $6988.89
monthly: i 1012% .833%, n 12 2 24
M P(1 i ) n $32000(1.00833) 24 $39052.20
I M P $39052.20 $32000 $7052.20
13.2 Daily and Continuous
Compounding
• Daily