Material Taken From:
Mathematics
for the international student
Mathematical Studies SL
Mal Coad, Glen Whiffen, John Owen, Robert Haese,
Sandra Haese and Mark Bruce
Haese and Haese Publications, 2004
Section 13C – Compound Interest
Example from the BrainPop video
6% yearly compound interest
Year 1 Year 2 Year 3 Year 4
capital
$50
$53.00 $56.18 $59.55
interest
$3.00
new
amount
$53.00 $56.18 $59.55 $63.12
$3.18
$3.37
$3.57
6% yearly compound interest
capital
Year 1 $50
interest
new amount
$3.00 $53.00
=$50×1.06
Year 2 $53.00 $3.18 $56.18
=$50×1.06×1.06
=$50×(1.06)2
Year 3 $56.18 $3.37 $59.55
=$50×1.06×1.06×1.06
=$50×(1.06)3
Year 4 $59.55 $3.57 $63.12
=$50×1.06×1.06×1.06×1.06
=$50×(1.06)4
6% yearly compound interest
capital
interest
new amount
Year 4 $59.55 $3.57 $63.12
=$50×1.06×1.06×1.06×1.06
=$50×(1.06)4
Recognize the connection to a geometric sequence:
Un + 1 = u1 rn
Example from the BrainPop Video
6% yearly compound interest
Year 4
=$63.12
=$50×1.06×1.06×1.06×1.06
=$50 (1.06)4
=$50(1 + 0.06)4
A = C  ( 1 + r/100 )n
Compound Interest Formulae
A = C  ( 1 + r/100 )n
A = future value
C = capital
r = interest rate
n = # of years
A = C  ( 1 + r/100k )nk
A = future value
C = capital
r = interest rate
n = # of years
k = # of compoundings in a year
From the Formula Booklet
Different Compounding Periods
Compounding
period
yearly
half-yearly
quarterly
monthly
daily
1 times per year
k=1
2 times per year
k=2
4 times per year
k=4
12 times per year
k = 12
365 times per year k = 365
From the Subject Guide
Example 1
To how much will $1000 grow to if it is invested at
12% p.a. for 9 years, compounding annually?
Example 2
A bank advertises an annual interest rate of 13.5%
p.a. but adds interest to the account monthly, giving
a monthly interest rate of 1.125%. Scott deposits
$3500 with the bank. How much will he withdraw
in 20 months time?
Example 3
To what amount will $900 grow to if it is invested at
10% p.a. for 7 years, compounding every 6 months?
Example 4
How long will it take $2000 to amount to $4300 if
invested at 8% p.a., with interest compounded annually?
Use the calculator (find the intersection)
Example 5
You want to have $5000 after 2 years. Find the
amount you should deposit if the account pays
2.5% annual interest compounded monthly.
Example 6
If Iman deposits $5000 in an account that compounds
interest quarterly and 2.5 years later the account totals
$6000, what rate of interest was paid?
Section 13D - Depreciation
• The loss in value over time
• The r-value is negative
A = C  ( 1 + r/100k )nk
A = future value
C = capital
r = interest rate
n = # of years
k = # of compoundings in a year
Example 7
An industrial dishwasher was purchased for ₤2400
and depreciated at 15% each year.
a) Find it’s value after six years.
b) By how much did it depreciate?
Example 8
Use the calculator to determine if it is better to invest
$1000 at 9% p.a., compounded semiannually or
$1500 at 6.5% simple interest.
Calculator
• You may choose to use the Finance application
on your calculator.
• Read Investigation 1 on page 434 for
instructions.
Homework
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13C.1 #3
13C.2 #3
13C.3 #1,2, 4
13C.5 #1, 5
13C.6 #1, 3
13C.7 #2