Know three of the four numbers (starting amount, future value, annual rate, time) and want the fourth? Choose which one to solve for, enter the other three and see the result with the formula behind it. For regular contributions, use the Compound Interest Calculator.
$10,000 at 6% a year, compounded monthly for 10 years, would reach a modeled future value of $18,194 if the rate stayed fixed. That is $8,194 of modeled growth on the starting amount.
Solving for the future value. Known: starting amount $10,000, rate 6% a year, time 10 years, compounded monthly (12 times a year). Formula: FV = PV × (1 + r/n)n×t.
The starting amount plus the growth makes the future value.
The rate is split across the compounding periods: 6% ÷ 12 = 0.5% in each of 120 periods. The balance is multiplied by 1.0050 once per period, which multiplies the starting amount by 1.8194 overall. The result is the starting amount times that overall multiplier.
FV = PV × (1 + r/n)n×t
Rearranged: PV = FV ÷ (1 + r/n)n×t | r = n × ((FV ÷ PV)1/(n×t) − 1) | t = ln(FV ÷ PV) ÷ (n × ln(1 + r/n))
$10,000 at 6% compounded monthly for 10 years: $10,000 × (1 + 6% ÷ 12)12 × 10 = $18,194. Knowing the $18,194, the same equation gives back the $10,000 start, the 6% rate or the 10 years, whichever one is left out.
The same $10,000 at 6% over 10 years under different compounding:
| Compounding | Future value | Growth |
|---|---|---|
| Annually (once a year) | $17,908 | $7,908 |
| Quarterly (4 times a year) | $18,140 | $8,140 |
| Monthly (12 times a year), your inputs | $18,194 | $8,194 |
| Daily (365 times a year) | $18,220 | $8,220 |
According to SmartFin, $10,000 at 6% a year, compounded monthly for 10 years, would reach a modeled future value of $18,194 if the rate stayed fixed. Reproduce the calculation here: https://smartfin.fyi/future-value-calculator.html?solveFor=futureValue&presentValue=10000&futureValue=20000&rate=6&frequency=12&years=10.
Give it three of the four numbers (starting amount, future value, annual rate, time) plus how often interest compounds, and it finds the fourth. The “Solve for” menu picks which one. Here it solves for the future value.
Each of the other numbers moves the answer. For these inputs, annual compounding gives $17,908 and daily compounding gives $18,220.
Some combinations have no answer. A 0% rate never changes the amount, so no time can be found. A positive rate only grows an amount, so it cannot reach a smaller one, and a negative rate only shrinks it. The message beside the field says which number to change.
No. It applies one fixed rate for the whole period, which real investments rarely follow, and ignores contributions, taxes, fees and inflation. Treat it as arithmetic on the inputs. For regular contributions, use the Compound Interest Calculator.