Week 6 Class 1&2
Point of focus: Introduction to compound interest
Learning intentions: Understand how compound interest works
Recap of simple interest
T= 3
T= 2
p2 r
T= 1
T= 0
p
pr
+Pr
Principal
Initial principal
amount (invested
or loaned)
p
Interest 1
Principal
p1 r
pr
Interest 2
pr
Interest 1
+Pr
p
pr
Principal
+Pr
p
Interest 3
Interest 2
Interest 1
Principal
A
Compound interest
Compound interest is generated when simple interest is added to
the principal at regular interval (monthly, yearly and etc.).
You earn interest on the principal plus any interest that has built up.
So that the amount of money used for calculating the interest
continues to increase overtime (must pay interest on interest)
T= 3
Compound interest
p3 r
T= 2
p2 r
T= 1
T= 0
p
Principal
Initial principal
amount (invested
or loaned)
p1 r
p1 p
p1 r
Interest 1
Principal
p2 p
P2= P1 + Interest 1
p2 r
Interest 2
Interest 1
p3
p1 r
p
Principal
P3= P2+ Interest 2
Interest 3
Interest 2
Interest 1
A
Principal
P4= P2+ Interest 3
Therefore…
Example 1: You invest $500 in a savings account with a 4% annual interest rate,
compounded annually, for 3 years. Use the simple interest formula to calculate the
following accounts:
a) The compounded value after 1 year
b) The compounded value after 2 year
Initial principal (P1) = $500
P2 = $520
r = 4%=
4
100
= 0.04
T = 1 Year
Simple interest formula : I1 = P1rT
I1 = 500 x 0.04x1 = $20
Compounded value (A1) = 500+20 =
$520
r = 4%=
T = 1 year
4
100
= 0.04
Simple interest formula : I2 = P2rT
I2 = 520 x 0.04x1 =$ 20.8
Compounded values (A2) = 520+20.8 = $540.8
Continuation
c) The compounded value after 3 year
To find the amount of compound interest
P3 = $540.8
earned after 3 years : Initial principal (p1)
r= 4%=
4
100
= 0.04
T = 1 Year
Simple interest formula : I1 = P1rT
I3 = 540.8 x 0.04x1 = $ 21.6
Compounded value (A3) = 540.8+21.6 =
$ 562.4
- Compound value (after 3 years)
I = A (3year)s – P1
I= $562.4 - $500 = $62.4
Example 2: An amount of 20,000 is invested at 4%p.a. with interest calculated at the end of
each year and added to the principal amount. Use the simple interest formula to calculate
the following amounts:
a) The compounded value after 1 year
Initial principal (P1) = $20,000
r = 4%=
4
100
= 0.04
b) The compounded value after 2 year
P2 = $2800
r = 4%=
4
100
= 0.04
T = 1 Year
T = 1 year
Simple interest formula : I1 = P1rT
• Simple interest formula : I2 = P2rT
I1 = 2 0,000 x 0.04x1 = $800
I2 =2800 x 0.04x1 =$ 832
Compounded value (A1) = 20000+800 =
Compounded values (A2) = 2800+832
$2800
= $21632
Continuation
c) The compounded value after 3 year
P3 = $ 21632
r= 4%=
4
100
= 0.04
T = 1 Year
Simple interest formula : I1 = P1rT
I3 = 21632 x 0.04x1 = $ 865.28
Compounded value (A3) = 21632 +
865.28 = $ 22497.28
Find the compound interest after 3
years
I = A (3years) – P1
I= $ 22497.28- $ 20,000= $2497.28