Compound Interest

1
Compound Interest
Amount invested 1000
Interest Rate 5
Method 1
Interest at end of Year 1
5 of 1000
50
0.05 x 1000
Amount at end of Year 1
1050
Interest at end of Year 2
5 of 1050
52.50
0.05 x 1050
Amount at end of Year 2
1050 52.50
1102.50
and so on
2
Compound Interest
Amount invested 1000
Interest Rate 5
Method 2
Amount at end of Year 1
105 of 1000
1.05 x 1000
1050
1102.50
Amount at end of Year 2
1.05 x 1050
and so on
3
Example Compound Interest
1000 invested at 5 interest
End of Year n Amount A()
0 1000.00
1
2
3
4
5
1050.00
1102.50
1157.63
1215.51
1276.28
4
Compound Interest
Amount invested 1000
Interest Rate 5
Method 3
1.05n x 1000
Amount at end of Year n
1.052 x 1000
1102.50
Amount at end of Year 2
1.0510 x 1000
1628.89
Amount at end of Year 10
5
General Formulae
Exponential Growth
k, a and m positive
a gt 1
y ka mx
Example Compound Interest
A 1.05n x 1000
x is n
y is A
a 1.05
k 1000
m 1
Can be written in other forms
A 1.10250.5n x 1000
k 1000
m 0.5
a 1.1025
6
Example Radioactive Decay
Plutonium has a half-life of 24 thousand years
Number of half-lives Time (000s years) Amount (g)
0 0 1000
1
2
3
4
5
500
24
250
48
125
72
62.5
96
120
31.25
7
Example Radioactive Decay of Plutonium
Decay functions
A 1000 x 0.5n where n no. of half lives
A 1000 x 2-n where n no. of half lives
A 1000 x 2-t/24 where t time in thousands
of years
Exponential Decay
a lt 1
m positive
k and a positive
y ka mx
a gt 1
m negative
8
General Shape of Graphs
Exponential Growth
Exponential Decay