Future Value Calculator
What a present amount and regular payments grow to at any compounding frequency, from annual to continuous, with the effective annual rate.
Result
Future value: $18,193.97
At a fixed rate for the whole period. Nothing is rounded until the result is shown.
- Interest earned
- $8,193.97
- Total paid in
- $10,000.00
- Effective annual rate
- 6.1678%
- Growth multiple
- 1.8194
https://calcgallery.com/time-value/future-value-calculator/
Results are arithmetic on the returns, rates and horizons you enter, not a forecast and not investment, tax or retirement advice. The site supplies no expected return, inflation rate, contribution limit, tax rate or withdrawal rate. Real returns vary from year to year, and fees, taxes and the order of returns all change the outcome. Check anything that matters with a qualified adviser. Read the full disclaimer
How to use the Future Value Calculator
- Enter the amount you have now and, optionally, a payment you add every period.
- Enter the annual interest rate, the number of years and how often interest compounds.
- Choose whether payments go in at the start or the end of each period, and read the future value.
The formula
With a present value PV, a payment PMT each period, an annual rate r compounded m times a year, and t years:
FV = PV × (1 + r/m)^(m×t) + PMT × ((1 + r/m)^n − 1) ÷ (r/m)where n is the number of whole payment periods. At a 0% rate the payment term is simply PMT × n. Payments at the start of each period multiply that term by (1 + r/m).
Continuous compounding
As interest is added more and more often, (1 + r/m)^m approaches e^r, where e is about 2.71828. Continuous compounding is that limit: FV = PV × e^(r×t). It is the most any rate can earn from compounding frequency alone. With continuous compounding the page takes payments once a year.
Agreement with the compound interest calculator
For a single amount compounded monthly, quarterly or yearly, this page and the compound interest calculator give the same answer to the cent. They use the same convention: the annual rate divided by the number of periods in a year.
With your numbers
- $10,000.00 at 6% for 20 years, effective 6.1678% a year
- Future value = $264,122.49, of which $130,000.00 was paid in
Quick reference
At a fixed rate for the whole period. Nothing is rounded until the result is shown.
| Example | Future value |
|---|---|
| 10,000 at 6% for 10 years, annually | $17,908.48 |
| Same, monthly | $18,193.97 |
| Same, continuously | $18,221.19 |
| 500 a month at 6% for 20 years | $231,020.45 |
| 10,000 and 500 a month at 0% | $130,000.00 |
| 10,000 and 500 at the start of each month | $265,277.59 |
Common questions about the Future Value Calculator
- What is the difference between the nominal and the effective rate?
- The nominal rate is the annual rate as quoted. The effective rate is what you actually earn over a year once interest is added more than once. 6% compounded monthly adds 0.5% a month, and twelve months of that come to 6.1678% for the year.
- Does compounding frequency matter much?
- Less than people expect, and less the more often it happens. 10,000 at 6% for 10 years grows to 17,908.48 compounded yearly, 18,193.97 monthly and 18,221.19 continuously. The step from yearly to monthly is worth far more than the step from monthly to continuous.
- What is an annuity due?
- A series of payments made at the start of each period rather than the end, like rent. Each payment earns one more period of interest, so the future value is higher by a factor of one plus the periodic rate.
- Why does my bank quote APY?
- Because in the US, Regulation DD requires deposit accounts to state an annual percentage yield, which is the effective rate. It lets you compare accounts that compound at different frequencies. The CD calculator converts between the two.