1. Financial Applications -Compound Interest
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2. What is Compound Interest?
Recall:
Simple Interest – Interest is earned on the original sum of money invested. Any interest previously earned does not earn interest.
Compound Interest – Interest is reinvested at regular intervals. The interest is added to the principal to earn interest for the next interval of time, or compounding period.

3. Simple vs Compound Interest
If you invest $100 and get interest 10% per year,
Simple
Interest
You will have ______ in 1 year.
$110
______ in 2 years.
$120
______ in 3 years.
$130
Compound
Interest
You will have ______ in 1 year.
$110
______ in 2 years.
$121
$110 + (10% of $110) 
______ in 3 years.
$133.1
$121 + (10% of $121) 

4. Compound Interest formula
The formula used in compound interest is
Amount (A) .
Principal (P)
Interest rate per period (i)
Number of compounding periods involved (n)

5. Compound periods
Number of compounding periods depends on how many times per year the interest is compounded.
How often interest is compounded
Effective Rate
r = annual interest rate
# of compounding periods in t years
Annually
Once / year
i = r
n = t
Semi-annually
Twice / year
i = r / 2
n = 2t
Quarterly
4 times / year
i = r / 4
n = 4t
Monthly
12 times / year
i = r / 12
n = 12t
Daily
365 times / year
i = r / 365
n = 365t

6. Example 1 – Compound Interest
To take a technology course, Mark borrows $3000 at an interest rate of 4.75% per annum, compounded annually. He plans to pay back the loan in 5 years. a) How much will Mark owe after 5 years? b) How much interest will Mark pay for the loan?
Compounded annually
Therefore, Mark will owe $ after 5 years.
b) Interest: (Cost of borrow)
=$ $3000
=$783.48

7. Example 2 – Compound Interest
$10000 is invested for five years at 6% per annum compounded semi- annually. a) Determine the amount of the investment at the end of the 5 years. b) Determine the interest earned in the five years.
Compounded semi-annually
Therefore, the amount of the investment will be $ after 5 years.
b) Interest earned:
=$ $10000 =$
10 semi-annuals in 5 years

8. Example 3 – Compound Interest
Joe buys a new sofa priced at $800. He can pay $800 now or not make any payment now and pay $950 in one year. The salesperson tells Joe that in effect he will have a loan of $800 for one year, compounded monthly. What is the monthly interest rate that Joe would be paying? or
Therefore, the monthly interest rate (i) is 1.44%;.
Compounded monthly
and the annual interest rate (r) is
17.3% per annum.
12 months
in 1 year

9. Example 4 – Finding the Period
Approximately how long would it take for a $15000 investment to double if it earns 15.6%/annum interest compounded weekly? or
Therefore, it will take approx weeks or
Compounded weekly
approx years to double!!
52 weeks in 1 year

10. Recall: Simple vs Compound Interest
If you invest $100 and get interest 10% per year,
Simple
Interest
You will have ______ in 1 year.
$110
______ in 2 years.
$120
______ in 3 years.
$130
Compound
Interest
You will have ______ in 1 year.
$110
______ in 2 years.
$121
$110 + (10% of $110) 
______ in 3 years.
$133.1
$121 + (10% of $121) 
Using the formula

11. Homework:
WS: Compound Interest