This note explains briefly two concepts concerning the time-value-of-money, namely future and present value. Careful application of these concepts will help you evaluate investment/financing situations such as real estate, life insurance, monthly payments on a car, and many others.
Future value is simply the sum to which a dollar amount invested today will grow given some appreciation rate.
To compute the future value of a sum invested today, the formula for interest that is compounded monthly is:
fv = principal * (1 + rrate/12) ** (12 * termy)
For interest that is compounded annually, use the formula:
fv = principal * (1 + rrate) ** (termy)
Note that the formula for future value is the formula from Case 1 of present value (below), but solved for the future-sum rather than the present value.
Present value is the value in today's dollars assigned to an amount of money in the future, based on some estimate rate-of-return over the long-term. In this analysis, rate-of-return is calculated based on monthly compounding.
Two cases of present value are discussed next. Case 1 involves a
single sum that stays invested over time. Case 2 involves a cash stream that
is paid regularly over time (e.g., rent payments), and requires that you
also calculate the effects of inflation.
Case 1a: Present value of money invested over time. This
tells you what a future sum is worth today, given some rate of return over
the time between now and the future. Another way to read this is that you
must invest the present value today at the rate-of-return to have some future
sum in some years from now (but this only considers the raw dollars, not
the purchasing power).
To compute the present value of an invested sum, the formula for interest that is compounded annually is:
Case 1b: This formulation can also be used to estimate the effects of inflation; i.e., compute real purchasing power of present and future sums. Simply use an estimated rate of inflation instead of a rate of return for the rrate variable in the equation.
Case 2: Present value of a cash stream. This tells you the cost in today's dollars of money that you pay over time. Basically, the money you pay in 10 years is worth less than that which you pay tomorrow, and this equation lets you compute just how much.
To compute the present value of a cash stream of monthly payments, the formula is: