Future Value: Formula, Examples and How to Calculate It
Where FV = PV(1 + r)^n actually comes from, how the contribution term attaches to it, and how to check a result by hand.
Written analysis of the arithmetic the calculators run: where the formulas come from, which assumptions dominate a result, and how to read a projection without being misled by it.
Where FV = PV(1 + r)^n actually comes from, how the contribution term attaches to it, and how to check a result by hand.
Present value is what a later amount is worth today. Future value is what today's amount becomes later. One equation solved in opposite directions: use present value to price an offer you are given, future value to project a plan you are making, and move both cash flows to the same date before comparing them.
Each deposit compounds for a different length of time. Summing that series is what the annuity factor does.
One is how the balance grows, the other is what it grows to. Confusing them makes rate quotes hard to compare.
A projection in future dollars answers a question nobody asked. Converting it to today's money is one division.
The target and the deadline determine the deposit. Here is the arithmetic, and what to change when the answer is too large.
The whole difference is one period of growth, applied to every deposit. That makes it small, predictable and free.
A one-point change in an assumption nobody can observe moves a 30-year projection by a quarter. That is a reason to run scenarios.
Retirement projection is future value on a long horizon, with two complications: inflation, and the fact that the target is an income rather than a sum.
A single reference table for what $10,000 becomes, with the arithmetic shown so you can check any cell.
Each article explains one part of the math that the calculators apply, with worked figures produced by the same engines that power the tools. Where an article shows a table, that table was generated from the calculation modules rather than typed by hand.
If you want the number rather than the explanation, start with the future value calculator or browse the full tool list.