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:**

**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:

· And then continue to the following year:

· etc...

**$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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