Ending investment value and modeled gain
The future value applies the selected periodic rate for the full holding period. Gain is ending value minus the original amount. Initial investment mode discounts the future target using the selected rate, holding period and compounding schedule. The annual table includes the fractional final year when applicable; at zero years it shows the initial amount.
To model fixed monthly investments rather than a single deposit, use the SIP Calculator and choose when contributions are made.
The formula
P is the one-time principal, r is annual return as a decimal, n is compounding periods per year, and t is years. An entered 10% becomes 0.10. Market returns do not compound at a fixed schedule. For an initial-investment target, P = future target ÷ (1 + r/n)^(n×t). Targets are future nominal amounts. Zero years or zero return gives an initial amount equal to the target.
Worked example
A one-time 10,000 amount at 10% compounded annually for three years grows to 13,310, a 33.1% total return and 1.331× value multiple.
How to use this calculator
- Choose Future value or Initial investment, and enter the starting amount or future target.
- Enter the holding period and annual return assumption; choose compounding frequency in additional options. Use annual frequency for an effective annual growth rate.
- Review the live ending value, amount invested, gain or loss and value multiple. Open the yearly table to see the modeled path.
Lump sum and periodic investing
A lump sum puts the full amount to work at the beginning. A SIP or contribution plan spreads entry dates across time.
The preferable approach depends on available cash, risk, behavior, and product terms—not this formula alone.
Frequency and quoted returns
More frequent compounding raises value when a positive nominal rate is divided into periods. Investment performance is often reported as an effective return instead.
Choose annual frequency when the rate already describes annual portfolio growth.
Assumptions & limitations
What this calculation assumes
- One initial amount and no cash flows.
- Fixed nominal annual rate.
- Reinvestment with no fees or tax.
What to keep in mind
- Volatility and sequence of returns are hidden.
- Daily compounding may not match an investment product.
- A modeled return is not guaranteed.
- Extremely large compounding combinations and inverse amounts above the supported input range are rejected.
Common questions
What does 1.5× mean?
The ending value is one and a half times the starting amount.
Which frequency should I choose for an annual investment return?
Choose annual compounding for an effective annual growth assumption. A 10% rate then grows 100 to 110 after a year. Choosing monthly treats 10% as a nominal rate divided into twelve periods and gives about 110.47, a different assumption.
Can I model a loss?
Yes, use a negative annual return above −100%.
How do I find the lump sum needed for a future target?
Choose Initial investment and enter the desired future value, return and holding period. The result discounts that target using the chosen frequency. A negative return can require a starting amount larger than the target; no later deposits are assumed.
Sources & further reading
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