What is the time-value of money? It is an estimate of what particular sum of money will be worth within a particular time-frame. From this you can see what needs to be done to achieve your goals.

There are two categories to this:

1. Future Value of Money: How much a particular present amount will be worth after a particular time at a particular interest rate.
2. Present Value of Money: How much an amount in a particular period is worth today at a particular interest rate.

Each category can be further broken down into an annuity or a single amount. An annuity is an amount paid in at the end of each compounding period. This makes comparing single amounts and and annuities difficult to compare with conventional equations.

The traditional equation for the future value of an annuity is , it can be converted from end of period payment to start of period payment by multiplying by , resulting in . In order to compare these, we also need the equation for the single amount, which is .

If you want to put away a certain total principle, it is far more powerful to take that amount and deposit it all at once, rather than as an annuity over the same period of savings. For example (see a chart here), an annuity of $1 per year for 40 years ($40 total) at 6% APR will grow to $165, but if you take that $40 and deposit all at once, at the same rate and period, it will grow to $411. That’s 2.5 times more than as an annuity and over 1000% growth compared to 400% for the annuity. This is not to say that annuities are bad, but shows how time can have a significant impact on a total particular principle.