Compound Interest
homework
•Worksheet: Compound Interests
Does anyone have any interest ininterest?
Very few banks today pay interest based onthe simple interest formula.  Instead, theypay interest by using a principle calledcompounding.
The difference between simple and compoundinterest is this:  Simple interest growsslowly, compounding speeds up the process.
How it works.
Simple interest is interest on the principleamount.
Compound interest is when your principle andany earned interest both earn interest.
Consider this example: You beginwith $100 invested at 10% annual interest.
After
Simple Interest
CompoundInterest
1 year
110
110
2 years
120
121
3 years
130
133
4 years
140
146
5 years
150
161
10 years
200
259
20 years
300
672
50 years
600
11,739
Compound Interest Wins!!
From this example, it is easy to see that if youare saving money, you would prefercompound interest.
Convert Percent into Decimals
•56.35%
•0.034%
•7.8%
•1%
P is the principal amount (starting amount)
r is the annual interest rate
m is the number of times interest is compoundedper year
t is the number of years
Calculate compound interest using thisformula:
A—Total amount
p —principle
r —interest rate
n —number of compounding periods
t —time in years
Compounding Period
Annually m=1
Semiannually  m=2
Quarterly  m=4
Daily  m=365
Example 1: Suppose $1000 is invested at 6% for 1 year. P = 1000 r = .06 t = 1 year If interest is compounded annually (m = 1), then the amount in the account at the end of the year is A = P(1 + 𝑟 𝑚 )mt = 1000(1 + 0.6 1 )(1)(1) = 1060
If interest is compounded quarterly, then the amount in the account at the end of the year is A = P(1 + 𝑟 𝑚 )mt = 1000(1 + 0.6 4 )(4)(1) = 1061.36
Example 2:
Find the final amount of a $100 investment after10 years at 5% interest compounded annually,quarterly, and daily.
Compounding
period
m
Final amount
Annually
Quarterly
Daily
C:\Users\Th\Desktop\IMG_6189.JPG
Example 3:
Find the final amount of a $2000 certificate ofdeposit (CD) after 5 years at an annual interestrate of 5.51% compounded annually?
Compounding
period
m
Final amount
Calculate compound interest using thisformula:
A—Total amount
p —principle
r —interest rate
n —number of compounding periods
t —time in years
Example:  $100 is invested at 10% interestcompounded yearly for 6 years
177.16
$250 invested at 6.5% for 8 yearscompounded monthly.
419.92
Example……
•$500 invested at 12% for 10 yearscompounded yearly.
Answer……
•Problem:
•$500 invested at 12% for10 years compoundedyearly.
•Answer:
Example……
•$1000 at 7.25% for 9 years compoundedmonthly.
Answer……
•Problem:
•$1000 at 7.25% for 9years compoundedmonthly.
•Answer:
Try these:
1.$750 at 6.5% for 5 years compounded annually
2.$25,000 at 8% for 3 years compounded annually
3.$680 at 5.5% for 1.5 years compounded monthly
4.$1500 at 4.5% for 2 years compounded monthly
•Problem:
•$750 at 6.5% for 5 yearscompounded annually
•Answer:
•Problem:
•$25,000 at 8% for 3 yearscompounded annually
•Answer:
•Problem:
1.$680 at 5.5% for 1.5 yearscompounded monthly
•Answer:
•Problem:
•$1500 at 4.5% for 2 yearscompounded monthly
•Answer: