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