Some money is deposited once and then left alone: a windfall parked in a CD, a gift to a child’s account, a bond held to maturity, a retirement rollover. For these single deposits, future value depends on just three things — the rate, the time and how often interest compounds. This calculator shows the result and then lines up every compounding frequency from annual to continuous, so you can see how much (or how little) that last factor matters.
How to use the lump sum calculator
- Enter the amount invested today.
- Enter the annual interest rate (the nominal rate, or APR).
- Choose the compounding frequency, from annually to continuously.
- Enter the number of years; decimals are fine.
You get the future value, total interest, growth multiple, effective annual rate and doubling time, followed by a compounding comparison and a year-by-year table.
Lump sum future value formulas
For interest compounded m times a year:
As m grows without limit, the expression approaches continuous compounding:
e ≈ 2.71828 is the base of natural logarithms. Continuous compounding is the theoretical ceiling for a given nominal rate and is widely used in finance theory and option pricing.
Worked example
You invest $10,000 at 6% compounded monthly for 15 years.
- Rate per month: 6% ÷ 12 = 0.5%
- Compounding periods: 12 × 15 = 180
- FV = $10,000 × 1.005180 = $10,000 × 2.454094 = $24,540.94
- Interest earned: $14,540.94; effective annual rate 6.1678%; doubling time 11.58 years
Does compounding frequency matter?
The same $10,000 at 6% for 15 years:
| Compounding | Future value | Effective annual rate |
|---|---|---|
| Annually | $23,965.58 | 6.0000% |
| Semi-annually | $24,272.62 | 6.0900% |
| Quarterly | $24,432.20 | 6.1364% |
| Monthly | $24,540.94 | 6.1678% |
| Weekly | $24,583.27 | 6.1800% |
| Daily | $24,594.21 | 6.1831% |
| Continuously | $24,596.03 | 6.1837% |
The jump from annual to monthly compounding is worth about $575; everything beyond monthly adds only about $55 more. When comparing accounts, look at the effective rate (APY) — it already folds compounding in.
Rate and time do the heavy lifting
Compounding frequency is a fine-tuning knob; rate and time are the main dials. Doubling the time horizon more than doubles the interest, because the growth factor is exponential: at 6% compounded monthly, $10,000 grows to $13,488.50 in 5 years but to $24,540.94 in 15. A quick way to sense these numbers is the rule of 72: divide 72 by the rate to estimate the years to double.
To go the other way — from a target future amount back to what you need today — use the present value of a future sum calculator. If you will keep adding money, the future value calculator handles regular payments too, and the future value table lists growth factors for a whole grid of rates and periods.
Figures assume a constant rate with no withdrawals, fees or taxes. They are estimates, not financial advice.
Frequently asked questions
What is the formula for the future value of a lump sum?
FV = PV × (1 + r ÷ m)^(m × t), where r is the annual rate, m the number of compounding periods per year and t the number of years. With continuous compounding it becomes FV = PV × e^(r × t).
How much difference does compounding frequency make?
Less than most people expect. $10,000 at 6% for 15 years grows to $23,965.58 with annual compounding and $24,596.03 with continuous compounding — a gap of about $630, or 2.6%. The rate and the number of years matter far more.
How long does it take to double a lump sum?
Divide ln(2) by ln(1 + effective annual rate). At 6% compounded monthly (6.1678% effective) a deposit doubles in about 11.58 years. The rule of 72 gives a quick estimate: 72 ÷ 6 = 12 years.
Can I enter a fraction of a year?
Yes. Enter years as a decimal, such as 2.5 for two and a half years. The calculator raises the growth factor to the fractional number of compounding periods.
What is the effective annual rate shown in the results?
It is the one-year growth rate after compounding — the same idea as APY. A 6% nominal rate compounded monthly is equivalent to 6.1678% compounded once a year.