When to use this formula
Use this formula when your inputs match the variables and units shown below. It is most useful for checking a calculator result, recreating the calculation in a spreadsheet or understanding which input has the biggest effect.
Quick use
Use the formulas to compare assumptions, not to predict markets. Show nominal and inflation-adjusted values separately when possible.
Formula
Future value = present value x (1 + r)^n; annuity future value = payment x (((1 + r)^n - 1) / r); present value = future value / (1 + r)^n; real return ≈ (1 + nominal return) / (1 + inflation) - 1.
Variables
r is the periodic return or discount rate, n is the number of periods and payment is the regular contribution or withdrawal amount.
Method notes
- Match contribution frequency to compounding frequency.
- Separate real and nominal returns.
- For retirement, test poor-return and high-inflation scenarios.
Example
10,000 invested for 20 years at 5% grows to about 26,533 before inflation, tax and fees.
Assumptions and limitations
Investment returns are uncertain. Taxes, fees, inflation, sequence risk, currency, pension rules and contribution limits can materially change retirement outcomes.
When the formula is not enough
- If the result depends on live prices, rates or official thresholds, check the latest value from the named source before relying on it.
- If the topic is medical, tax, legal, lending or safety related, use the result as a learning aid and check primary guidance before acting.
- If units or time periods differ, convert them before comparing results.
- If rounding affects the decision, keep extra precision until the final step.
Common mistakes
- Treating expected return as guaranteed.
- Ignoring inflation in long retirement projections.
- Mixing monthly contributions with annual compounding without conversion.
FAQ
Why look at the formula instead of only the answer?
The formula shows which inputs actually drive the result. That makes it easier to spot a wrong unit, compare two scenarios or explain the answer to someone else.
Can different calculators use different formulas for the same topic?
Yes. Some topics have multiple accepted methods or simplified variants. When that matters, the calculator should say which method it uses and what is excluded.
Are formula pages updated?
Stable math formulas need occasional review. Formulas that depend on changing rules, prices or thresholds need a dated source before the page can make stronger claims.