# 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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