# 5.16. Calculating Asset Appreciation (Future Value)

## Problem

You want to know how much
something will be worth in the future,
given its value today and an expected interest rate,
`i`

(for example, calculating the amount of money
you can accumulate in a savings account given an initial deposit).

## Solution

You must calculate the appreciation of an asset over time at the
assumed interest rate. This is often referred to as the
`future value`

of an asset. For a given interest
rate, `i`

, an asset appreciates by a factor of (1
+ `i`

) for each period (such as a year).

## Discussion

For the purposes of illustration, let’s calculate the future value of an asset using the brute-force method.

If you deposit $1 in a bank account that earns 5% interest per year, one year from now, you will have earned 5 cents in interest. The total account, including principal and interest, will be worth $1.05. The math for this is:

FV = PV * (1 + i);

where *FV* is the future value (the amount of
money you’ll have next year, sometimes called
*FV1*), *PV* is the
`present value`

(the amount of money you deposited
initially, sometimes called *FV0*), and
`i`

is the interest rate (expressed as a decimal,
such as 0.05).

So if you deposit $100 at a 5% interest rate, the future value at the end of one year is $105, which is determined as follows:

FV1 = 100 * (1 + .05);

Typically, interest is compounded over time, so at the end of the second year, the value is:

FV2 = FV1 * (1 + i);

Here is a function that calculates the future value by brute force for ...

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