Simple and Compound Interest
What is interest?
 Money earned/charged from an investment/loan
 Calculated with a rate (proportion of the principal
amount)
 Banks pay you interest for your investment
 you pay banks interest for loans
Simple Interest
 With simple interest, the interest is calculated at the
end of the year (interest rates are given as an annual
rate usually) on the original principal
 Next year the interest is calculated again on the
principal
 Essentially the interest earned is the same each year
 In real life, simple interest is not practical as it results
in a loss for businesses
Calculating Simple Interest
 The formula to calculate simple interest is:
I=Prt
 P= principal (original amount of loan or investment)
 I= Interest (the value of interest at the end of the time period)
 R= rate (the rate of the interest, on an annual basis, always
convert from percent to decimal when calculating with formula)
 T= time (years usually, sometimes it will have to be converted
according to the situation)
Calculating Simple Interest
 The formula to calculate the total value “amount” of
the interest and the principal value the formula is”
A= P+I
 A= total amount
 P= principal value
 I= Interest value
Example
 What would the value of a $4000 investment be after
7 years with interest at a rate of3%?
 I=Prt
 I=4000* 0.03* 7
 I=840
 A=P+I
 A=4000+840
 A=4840
 The value of the investment after 7 years will be 4840
Example
 What would the value of a $5000 investment be after
16 months with interest at a rate of 3.9%
 I=Prt
 I=5000* 0.039* (16/12)  since a year is 12 months
 I= 260
 A=P+I
 A=5000+260
 A=5260
 So the value of the investment after 16 months would
be $5260
Practice!
 What would the value of a $500 investment be after 8
years if invested at a rate of 4.8%
 Remember to calculate the total amount, not just the
interest
 Your answer should be $692
Practice!
 How much would you owe the bank if you took a loan
of $7000 at a rate of 9% for 28 months?
 Remember to convert the “time” unit into years
 You should have an answer of $8470
Compound Interest
 Compound interest is when the interest calculated is
calculated on the principal amount and the interest
added from the previous term
 This is a more commonly seen form of interest in the
real world
 It is also more profitable for investments as the
interest value is calculated on a larger sum
Calculating Compound Interest
The formula to calculate the value of compound
interest is:
𝒏
A= 𝑷 ∗ (𝟏 + 𝒓 ∗ 𝒕)
I= Interest
P=principal amount
R= rate
T= time for 1 compound period
N= number of compound periods
Calculating Compound Interest
 Compound interest can be calculated for different
time period as well, not just annually
Term
Meaning
Annually
Once a year
Semi-annually
Twice a year
Quarterly
4 times a year (3 months in each quarter)
Monthly
12 times a year
Weekly
52 times a year
Daily
365 times a year
Example
 What would the value of a $2000 bond be after 3
months at an interest rate of 5%
 I= 2000 (1+ 0.05* 1/12)^3 (the months are converted as
1/12 as there are 12 months in a year, but to calculate
for three months the exponent value is raised to 3)
 A= 2025.10
Example
 How much would you owe the bank for a loan of
$4000 compounded semi-annually for 4 years at an
interest rate of 7%?
 A= 4000* (1+ 0.07* ½)^8  semi annually makes the
denominator for “time” 2 as it is calculated twice a
year, whereas the exponent becomes 8 since in 4
years, if calculated twice each year the interest would
be compounded 8 time
 A= 5267.24
Practice!
 $2500 compounded quarterly for 5 years at a rate of
4.75%
 Remember to convert the “time” unit
 You should get $3165.76 as your answer
Resources
 http://www.youtube.com/watch?v=B3IdfBcXrLA
 http://www.youtube.com/watch?v=GtaoP0skPWc