Compound Interest methodology

Compound interest is the effect of earning returns on returns. When a balance grows, the next period's interest is calculated on the larger total, not just the original amount. The compound interest calculator turns this into a projection: it takes a starting balance, a regular contribution amount, an expected return, a compounding frequency, a contribution frequency, and a time horizon, and estimates a future balance.

What the calculator measures

The compound interest calculator measures the future value of a single lump sum plus a stream of equal contributions. It answers questions such as:

• How much will my savings be worth in 20 years?
• How much do I need to contribute each month to reach a target?
• What return rate would I need to hit a goal?
• How long will it take to reach a target balance?

It does not model taxes, fees, inflation, or changing contribution rates. It projects a single, smooth growth path.

Core formula and compounding frequencies

The calculator uses the standard future-value-of-an-annuity formula with end-of-period contributions.

When the compounding frequency and contribution frequency are the same, the familiar form is:

FV = PV(1 + r/n)^(nt) + PMT * (((1 + r/n)^(nt) - 1) / (r/n))

Where:

• FV = future value
• PV = present value (starting lump sum)
• PMT = regular contribution per period
• r = annual nominal return rate (as a decimal)
• n = number of compounding periods per year
• t = number of years

When compounding and contributions happen at different rates, the annual rate is first converted to an effective rate per contribution period:

r_eff = (1 + r/n)^(n/k) - 1

Where k is the number of contribution periods per year. The future value is then calculated with k * t periods and PMT = monthly × 12 / k per period:

FV = PV(1 + r_eff)^(kt) + PMT * (((1 + r_eff)^(kt) - 1) / r_eff)

The tool supports three compounding frequencies and four contribution frequencies:

Compounding frequency	n	Contribution frequency	k
Monthly	12	Weekly	52
Daily	365	Monthly	12
Annual	1	Quarterly	4
		Annual	1

End-of-period contributions

Contributions are treated as happening at the end of each contribution period. A contribution paid at the end of a month does not earn interest during that month. This is the standard convention for savings and pension projections.

End-of-period contributions produce a slightly lower result than beginning-of-period contributions. Beginning-of-period would give each contribution an extra period of growth. The calculator does not support beginning-of-period timing.

The contribution amount slider is always shown as a monthly figure. When you choose a different contribution frequency, the calculator converts the monthly amount to the matching per-period deposit. For example, a quarterly schedule with a 500 monthly amount becomes 500 × 12 / 4 = 1,500 paid every quarter.

Solve-for-any implementation

The calculator can solve for any one missing variable if the others are supplied. It uses a numerical search rather than a closed-form rearrangement when a closed form is awkward or does not exist.

Input	How it is solved
Future value	Direct formula evaluation
Present value	Direct formula rearrangement
Regular contribution	Direct formula rearrangement
Time	Bisection search on the full formula
Return rate	Bisection search on the full formula

Bisection starts with a wide bracket and repeatedly halves the interval until the result is within a small tolerance. The search is bounded by practical limits. For example, the rate search is bounded between 0% and 100% to avoid nonsensical results.

Assumptions and limitations

The calculator assumes:

• A fixed annual return rate for the entire horizon.
• A fixed contribution amount for the entire horizon.
• Contributions are made at the end of each period.
• No taxes, platform fees, fund charges, or inflation.
• The return rate stays constant even after the balance grows.

These assumptions are useful for planning but they are not realistic over long periods. Real returns vary from year to year. Fees and taxes reduce returns. Inflation reduces purchasing power. A person may change contributions or withdraw money early. The calculator shows a mathematically clean projection, not a forecast.

Worked check

Here is a closed-form check using the formula above.

Inputs: $10,000 starting balance, $500 contributed monthly, 7% annual return, monthly compounding, 20 years.

Part	Calculation	Result
Lump sum	$10,000 × (1 + 0.07/12)^(12 × 20)	$40,387.39
Contributions	$500 × (((1 + 0.07/12)^(240) - 1) / (0.07/12))	$260,463.33
Total future value	$40,387.39 + $260,463.33	$300,851.72
Total paid in	$10,000 + ($500 × 240)	$130,000.00
Growth from compounding	$300,851.72 - $130,000.00	$170,851.72

You can plug the same numbers into either the UK compound interest calculator or the US compound interest calculator and get the same result.

Sources and references

• Investor.gov, Compound Interest Calculator - US Securities and Exchange Commission.
• US Securities and Exchange Commission, "Saving and Investing," including compound interest basics.
• Bank of England, "Inflation and the economy," for context on nominal versus real returns.
• HM Revenue and Customs, ISA and SIPP guidance, for UK tax wrapper context.
• Internal Revenue Service, retirement plan and IRA guidance, for US tax wrapper context.

Last updated

This methodology was last reviewed on 10 August 2026.

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This methodology page is educational and is not financial advice.