Compound interest calculator

The formula

Compound interest with regular contributions combines two calculations:

A = P(1 + r/n)^(nt) + PMT × [ ((1 + r/n)^(nt) − 1) / (r/n) ]

The first term grows your starting balance. The second grows each contribution from the moment it is deposited. P is the starting amount, r the annual rate as a decimal, n the compounding periods per year, t the number of years and PMT the amount added each period.

This calculator assumes contributions are made at the end of each compounding period, which is the conservative convention and matches how most payroll and standing-order savings actually work.

A worked example

$10,000 to start, $200 added monthly, 7% a year, compounded monthly, for 20 years:

• Final balance: $144,573
• You contributed: $58,000
• Interest earned: $86,573

Interest accounts for 60% of the final balance. In year 1 the account grows by about $3,200, of which roughly $800 is interest on the opening $10,000. By year 20 the account gains about $12,058 in a single year - five times the $2,400 you put in. That gap between what the money earns and what you add is the whole point of starting early.

Why time beats amount

Two savers, both stopping at 65 with a 7% return:

Saver	Contributes	Total paid in	Balance at 65
Starts at 25, stops at 35	$500/month for 10 years	$60,000	$702,000
Starts at 35, never stops	$500/month for 30 years	$180,000	$610,000

The first saver pays in a third as much and still finishes almost $100,000 ahead. Nothing about the second saver’s behaviour is wrong - they simply had thirty years of compounding instead of forty. This is the most valuable and least intuitive fact in personal finance.

Compounding frequency, in perspective

$10,000 at 7% for 20 years, no contributions:

Frequency	Final balance
Annually	$38,697
Quarterly	$40,064
Monthly	$40,387
Daily	$40,551

The whole range spans under 5%. Choosing an account paying 7.2% compounded annually beats one paying 7% compounded daily. Chase the rate, not the frequency.

What this cannot tell you

Investment returns are not a fixed percentage - they arrive as a volatile sequence, and the order matters when you are withdrawing. This calculator models steady growth, which is the right tool for savings accounts, bonds and long-run planning, and a rough approximation for equities. It also ignores tax on interest, dividends and gains, plus platform and fund fees. Re-run the 20-year example at 6% instead of 7% to see what a single percentage point of annual fee costs - the balance falls from $144,573 to $125,510, a loss of just over $19,000.