5.16. Calculating Asset Appreciation (Future Value)
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).
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
i, an asset appreciates by a factor of (1
i) for each period (such as a year).
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 ...