Compound Interest

1
(No Transcript)
2

• Compound Interest

3

• Compound Interest
• Ill start with a brief reminder about
  percentages and simple interest.

4

• Compound Interest
• Ill start with a brief reminder about
  percentages and simple interest.
• Percentages always seem to cause trouble.

5

• Compound Interest
• Ill start with a brief reminder about
  percentages and simple interest.
• Percentages always seem to cause trouble.
• A number less than one can be expressed as a
• fraction such as 3/47 or, as a decimal, 0.064,
  which will be a
• number between 0 and 1.

6

• A percentage is just the same fraction

7

• A percentage is just the same fraction
• expressed as a number between 0 and 100

8

• A percentage is just the same fraction
• expressed as a number between 0 and 100
• which we get by by multiplying the fraction by
  100.

9

• A percentage is just the same fraction
• expressed as a number between 0 and 100
• which we get by by multiplying the fraction by
  100.
• In our example of (3/47)
• this would be a percentage of
• (3/47) x 100

10

• A percentage is just the same fraction
• expressed as a number between 0 and 100
• which we get by by multiplying the fraction by
  100.
• In our example of (3/47)
• this would be a percentage of
• (3/47) x 100
• 300/47
• about 6.4.

11

• A percentage is just the same fraction
• expressed as a number between 0 and 100
• which we get by by multiplying the fraction by
  100.
• In our example of (3/47)
• this would be a percentage of
• (3/47) x 100
• 300/47
• about 6.4.
• It is normal to use decimals, although values
  like 5½ etc are also used.

12

• E.g. 6.4 of 500
• is just the fraction 6.4/100 ( 0.064) of 500

13

• E.g. 6.4 of 500
• is just the fraction 6.4/100 ( 0.064) of 500
• 0.064 x 500 32

14

• E.g. 6.4 of 500
• is just the fraction 6.4/100 ( 0.064) of 500
• 0.064 x 500 32
• Simple interest involves the adding of a fixed
  of a lump sum at regular intervals (usually one
  year). 6.4 p.a. (per annum) for example.

15

• E.g. 6.4 of 500
• is just the fraction 6.4/100 ( 0.064) of 500
• 0.064 x 500 32
• Simple interest involves the adding of a fixed
  of a lump sum at regular intervals (usually one
  year). 6.4 p.a. (per annum) for example.
• For our example, this means that at the end of
  each year 32 in interest is added.

16

• E.g. 6.4 of 500
• is just the fraction 6.4/100 ( 0.064) of 500
• 0.064 x 500 32
• Simple interest involves the adding of a fixed
  of a lump sum at regular intervals (usually one
  year). 6.4 p.a. (per annum) for example.
• For our example, this means that at the end of
  each year 32 in interest is added. After one
  year the total becomes 532.

17

• E.g. 6.4 of 500
• is just the fraction 6.4/100 ( 0.064) of 500
• 0.064 x 500 32
• Simple interest involves the adding of a fixed
  of a lump sum at regular intervals (usually one
  year). 6.4 p.a. (per annum) for example.
• For our example, this means that at the end of
  each year 32 in interest is added. After one
  year the total becomes 532. After two years the
  interest would be another 32 and so the total
  becomes 564, etc.

18

• Compound interest

19

• Compound interest
• This involves the interest being added at the end
  of each year and this new, larger amount being
  the new lump sum for the ensuing year.

20

• Compound interest
• This involves the interest being added at the end
  of each year and this new, larger amount being
  the new lump sum for the ensuing year.
• This means that for our example, at the end of
  the second year the interest for that year would
  be 0.064 x 532 (the amount involved at the
  beginning of that year) x 0.064 34.05

21

• Compound interest
• This involves the interest being added at the end
  of each year and this new, larger amount being
  the new lump sum for the ensuing year.
• This means that for our example, at the end of
  the second year the interest for that year would
  be 0.064 x 532 (the amount involved at the
  beginning of that year) x 0.064 34.05
• We can write this as 532(1.064) or
  500(1.064)(1.064) 500(1.064)2.

22

• For another rate, say 8, a similar calculation
  would give a final amount of
• 500(1.08)4 after four years

23

• For another rate, say 8, a similar calculation
  would give a final amount of
• 500(1.08)4 after four years
• and the total interest is
• 500(1.084) 500

24

• For another rate, say 8, a similar calculation
  would give a final amount of
• 500(1.08)4 after four years
• and the total interest is
• 500(1.084) 500
• 500(1.3605) - 500

25

• For another rate, say 8, a similar calculation
  would give a final amount of
• 500(1.08)4 after four years
• and the total interest is
• 500(1.084) 500
• 500(1.3605) - 500
• 680.25 - 500

26

• For another rate, say 8, a similar calculation
  would give a final amount of
• 500(1.08)4 after four years
• and the total interest is
• 500(1.084) 500
• 500(1.3605) - 500
• 680.25 - 500
• 180.25

27

• For another rate, say 8, a similar calculation
  would give a final amount of
• 500(1.08)4 after four years
• and the total interest is
• 500(1.084) 500
• 500(1.3605) - 500
• 680.25 - 500
• 180.25
• As a of the original 500, this is
• (180.25 / 500) x 100

28

• For another rate, say 8, a similar calculation
  would give a final amount of
• 500(1.08)4 after four years
• and the total interest is
• 500(1.084) 500
• 500(1.3605) - 500
• 680.25 - 500
• 180.25
• As a of the original 500, this is
• (180.25 / 500) x 100
• 36

29

• For another rate, say 8, a similar calculation
  would give a final amount of
• 500(1.08)4 after four years
• and the total interest is
• 500(1.084) 500
• 500(1.3605) - 500
• 680.25 - 500
• 180.25
• As a of the original 500, this is
• (180.25 / 500) x 100
• 36
• For a simple interest calculation, the interest
  would have been 4 x 8 of 500 32 of 500
  160

30

• In general we have found the total amount owing
  from an initial amount P at a rate of r for a
  period of t years becomes

31

• In general we have found the total amount owing
  from an initial amount P at a rate of r for a
  period of t years becomes
• P(1 r/100)t

32

• In general we have found the total amount owing
  from an initial amount P at a rate of r for a
  period of t years becomes
• P(1 r/100)t
• This interest very rapidly gets large.

33

• In general we have found the total amount owing
  from an initial amount P at a rate of r for a
  period of t years becomes
• P(1 r/100)t
• This interest very rapidly gets large. If you
  borrow at a normal credit-card rate of 32 and do
  not pay off the amount owing for 5 years then the
  final amount owing would become P(1 (32/100))5
  P(1.32)5

34

• In general we have found the total amount owing
  from an initial amount P at a rate of r for a
  period of t years becomes
• P(1 r/100)t
• This interest very rapidly gets large. If you
  borrow at a normal credit-card rate of 32 and do
  not pay off the amount owing for 5 years then the
  final amount owing would become P(1 (32/100))5
  P(1.32)5
• P(4.007) P 3.007xP. The interest charge
  is over THREE times the original i.e. over 300
  interest!

35

• In general we have found the total amount owing
  from an initial amount P at a rate of r for a
  period of t years becomes
• P(1 r/100)t
• This interest very rapidly gets large. If you
  borrow at a normal credit-card rate of 32 and do
  not pay off the amount owing for 5 years then the
  final amount owing would become P(1 (32/100))5
  P(1.32)5
• P(4.007) P 3.007xP. The interest charge
  is over THREE times the original i.e. over 300
  interest!
• (Simple interest would bring a charge of 4x0.32xP
• 1.28xP bad enough)

36
(No Transcript)
37
(No Transcript)