What future value means
Future value (FV) is what an amount of money, or a series of payments, will be worth at a later date if it earns a given interest rate. It answers questions like "what will $5,000 become in 10 years at 4%?" or "what will I have if I add $200 a month for 15 years?"
You can use it for savings accounts, certificates of deposit, and any projection where you assume a fixed rate. The rate is an assumption you choose, not a promised return, so try a few different rates to see a range.
For a lump sum only, the main compound interest calculator works the same way. If your deposits are monthly and you want to focus on that case, see the monthly compound interest calculator.
The formulas
- Lump sum: FV = PV × (1 + r/n)n·t
- Regular payments at the end of each period (ordinary annuity): FV = PMT × ((1 + r/n)n·t − 1) / (r/n)
- Regular payments at the start of each period (annuity due): FV = PMT × ((1 + r/n)n·t − 1) / (r/n) × (1 + r/n)
- Lump sum plus payments: add the lump sum result and the payments result
- If r = 0: FV = PV + PMT × n·t
- Present value (the reverse): PV = FV / (1 + r/n)n·t
In these formulas, PV is the present value, PMT is the payment per period, r is the nominal annual rate as a decimal (5% is 0.05), n is the number of compounding periods per year and t is the number of years. In this calculator the payment frequency equals the compounding frequency, so monthly compounding means monthly payments.
Total contributions are PV + PMT × n·t, and total interest is FV minus total contributions.
Example scenarios
These are sample inputs to try in the calculator above.
| Scenario | Present value | Periodic payment | Annual rate | Compounding | Years | Payment timing | Future value | Total contributions | Total interest |
|---|---|---|---|---|---|---|---|---|---|
| Lump sum only | $10,000 | $0 | 5% | Annually | 10 | n/a | $16,289 | $10,000 | $6,289 |
| Monthly savings from zero | $0 | $250 | 4% | Monthly | 15 | End | $61,523 | $45,000 | $16,523 |
| Lump sum plus monthly payments | $5,000 | $200 | 6% | Monthly | 20 | End | $108,959 | $53,000 | $55,959 |
| Same payments, paid at the start | $5,000 | $200 | 6% | Monthly | 20 | Beginning | $109,421 | $53,000 | $56,421 |
Comparing the last two rows shows how much payment timing alone changes the outcome.
Future value vs present value
Future value looks forward: what money today becomes later. Present value looks backward: what a future amount is worth today, given a rate. The two use the same growth factor, (1 + r/n)n·t, one multiplying and the other dividing.
Use present value when you have a target. If you need a certain amount in 10 years, PV = FV / (1 + r/n)n·t tells you how much a single deposit today would have to be at your assumed rate. A higher rate or longer time lowers the amount you need to start with.
Payments at the start vs end of each period
With an ordinary annuity, each payment is made at the end of the period, so the first payment earns interest for one period fewer than with an annuity due. When payments are made at the start of each period, every payment earns one extra period of interest, which is why the payment part of the formula is multiplied by (1 + r/n). The lump sum is not affected by this choice.
Rate, compounding and inflation
The rate you enter is a nominal annual rate. More frequent compounding raises the result slightly for the same nominal rate, but the difference is usually small compared with the effect of the rate itself or the number of years.
Future value is also stated in future dollars. Prices usually rise over time, so the same amount buys less later. To adjust for that, run your numbers through the investment calculator with inflation. If you only know your starting and ending balances and want the yearly rate between them, use the growth rate calculator.