Transcript Learning Objectives for Sections 3.1-3.2 Simple & Compound Interest After this lecture, you should be able to  Compute simple interest using the.

Learning Objectives for Sections 3.1-3.2
Simple & Compound Interest
After this lecture, you should be able to
 Compute simple interest using the simple interest formula.
 Solve problems involving investments and the simple interest
formula.
 Compute compound interest.
1
Some Preliminary Notes
 Financial institutions often use 360 days for one year when computing
time.
 Time must be in terms of years to use in the formulas.
 All rates (%) must be converted to decimals to use in formulas.
 When an answer is rounded, use the symbol  instead of =.
 We will round to the nearest cent for dollar amounts, unless otherwise
stated.
 Try to avoid rounding until the final answer.
2
Conversions: Time Periods
Example 1: Convert the given time periods into years:
a) 180 days
b) 120 days
c) 3 quarters
d) 7 months
e) 60 days
f) 26 weeks
3
Conversions: Percents to Decimals
Example 2: Convert the given percents to decimals:
a) 4.5%
b) .32%
c) 112%
4
Conversions: Decimals to Percents
Example 3: Convert the given decimals to percents:
a) 0.06
b) 5
c) 0.11
5
Simple Interest Formula
Simple Interest Formula
where
I  P rt
I = interest
P = principal (amount invested or amount of loan)
r = annual simple interest rate (as a decimal)
t = time in years
6
An Example
Example 4: Find the interest on a boat
loan of $5,000 at 16% for 8 months.
Example 5: What is the total amount to be paid back on
the boat loan in Example 4?
7
Total Amount to Be Paid Back
 In general, the future value (amount) is given by the following
equation:
A = Principal + Interest
A=P+I
A = P + Prt
A = P (1 + rt)
8
Another Example
Example 6: Find the total amount due on a loan of $600 at 16%
interest at the end of 15 months.
9
Another Example
Example 7: A loan of $10,000 was repaid at the end of 6 months.
What amount (principal and interest) was repaid, if a 6.5% annual
rate of interest was charged?
10
Application
Example 8: A department store charges 18.6% interest (annual)
for overdue accounts. How much interest will be owed on a
$1,080 account that is 3 months overdue?
11
Purchase Price of a Note
Example 10: What is the purchase price of a 26-week T-bill
with a maturity value of $1,000 that earns an annual interest
rate of 4.903%?
12
Compound Interest
 Compound interest: Interest paid on interest reinvested.

Compound interest is always greater than or equal to simple
interest in the same time period, given the same annual rate.
13
Compounding Periods
The number of compounding periods per year (m):
 If the interest is compounded annually, then m = _______
 If the interest is compounded semiannually, then m = _______
 If the interest is compounded quarterly, then m = _______
 If the interest is compounded monthly, then m = _______
 If the interest is compounded daily, then m = _______
14
Example
Example 1: Suppose a principal of $1 was invested in an account
paying 6% annual interest compounded monthly. How much
would be in the account after one year?
The annual interest rate is 6%, so the monthly interest rate
would be:
0.06

12
In general, we can find the rate per compounding period as:
annual rate
# of com pounding periods per year
Continued on next slide.
15
Solution
 Solution: Using the Future Value with simple interest
formula A = P (1 + rt) we obtain the following amount:
 after one month:
 after two months:
 after three months:
After 12 months, the amount is: ________________________.
With simple interest, the amount after one year would be _______.
The difference becomes more noticeable after several years.
16
Graphical Illustration of
Compound Interest
The growth of $1 at 6% interest compounded monthly compared
to 6% simple interest over a 15-year period.
Dollars
The blue curve refers to the
$1 invested at 6% simple
interest.
The red curve refers to the
$1 at 6% being compounded
monthly.
Time (in years)
17
General Formula: Compound Interest
The formula for calculating the Future Amount with Compound
Interest is
mt
r 

A  P 1 

m

Where
A is the future amount,
P is the principal,
r is the annual interest rate as a decimal,
m is the number of compounding periods in one year, and
t is the total number of years.
18
Example
Example 2a: Find the amount to which $1,500 will grow if
compounded quarterly at 6.75% interest for 10 years.
Example 2b: Compare your answer from part a) to the amount
you would have if the interest was figured using the simple
interest formula.
19
Changing the number of
compounding periods per year
Example 3: To what amount will $1,500 grow if compounded
daily at 6.75% interest for 10 years?
20
Effect of Increasing the
Number of Compounding Periods
 If the number of compounding periods per year is increased
while the principal, annual rate of interest and total number of
years remain the same, the future amount of money will
increase slightly.
21
Example
Example 4: If $20,000 is invested at 4% compounded monthly,
what is the amount after a) 5 years b) 8 years?
22
Which is Better?
Example 5: Which is the better investment and why:
8% compounded quarterly or 8.3% compounded annually?
23
Inflation
Example 6: If the inflation rate averages 4% per year compounded
annually for the next 5 years, what will a car costing $17,000
now cost 5 years from now?
24