Future Value
Overview
The prsent value calculation works in reverse for future value. Supose you have 100 dollars today, you can determine how much the money would
be worth in the future. That is, you could put the money in the bank and receive it in a year, plus interest. We call this
the future value. Assuming that the interest rate is 10%, we calculate the future value as follows:
{% Future \; Value = 100 \times 1.1 %}
The above examples have been simplified by considering a single period. The analysis doesnt really change when dealing with multiple
periods. For insance, suppose we have cash today, and we want to caclulate the future value of the cash in 2 years. In essence, if
we are given a two year rate, the process is the same. However, in order to make comparisons between rates of different time periods,
it is common annualize all rates, that is, to quote them in terms of how much interest is paid per year, assuming that the interest
is reinvested each year. In this example, assume that the quoted annual rate is 10%. Then if I invest that money in the bank account,
after 1 year, I will have earned $10 interest, so my balance will be $110. Now, the earned $10 can also earn interest, so after year
2, I will have my $110 + 10% of 110. When calculating interest this way, the value after n periods will be
{% P_n = P_0(1+r)^n %}
These reflections show how you can take a cash flow, and "move" it to another date. This can be done with multiple cash flows at different dates, that
is, they can be combined into a single cash flow at a single point in time. The reverse can happen as well. A single cash flow can be split
into multiple cash flows at different points in time. This is useful if you have money today, for instance, but have varioius liabilities in
the future that you will pay from the cash you have today.
