Thursday, 29 November 2012

COMPOUND INTEREST


So, adding 10% interest is the same as multiplying by 1.10
Note: the Interest Rate was turned into a decimal by dividing by 100: 10% = 10/100 = 0.10, readPercentages to learn more, but in practice all you need to do is move the decimal point 2 places, so for example 12% ⇒ 1.2 ⇒ 0.12
So, now we have just one step:
  1. Multiply the "Loan at Start" by (1 + Interest Rate) to get "Loan at End"
(But remember the Interest Rate should be a decimal value first! 0.10, not 10%)
A simple calculation shows you they are the same:
$1,000 + ($1,000 x 10%) = $1,000 + $100 = $1,100
  
is the same as:$1,000 × 1.10 = $1,100
Now, here is the magic ...

... the same formula works for any year!

· We could do the next year like this: $1,100 × 1.10 = $1,210
· And then continue to the following year: $1,210 × 1.10 = $1,331
· etc...
So it works like this:

In fact we could go straight from the start to Year 5, if we multiply 5 times:

$1,000 × 1.10 × 1.10 × 1.10 × 1.10 × 1.10 = $1,610.51
But it is easier to write down a series of multiplies using Exponents (or Powers) like this:

The Formula

We have been using a real example, but let's be more general by using letters instead of numbers, like this:
(Can you see it is the same? Just with PV = $1,000, r = 0.10, n = 5, and FV = $1,610.51)
Here is is written with "FV" first:
FV = PV × (1+r)n
where FV = Future Value

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