Compound Interest Calculator

Why compound interest looks slow, then impossible

Compound interest is interest earned on interest. Simple to state, and almost impossible to feel until you see it on a chart.

Leave 10,000 alone at 7% a year, compounded monthly:

After	Balance
10 years	20,096.61
20 years	40,387.39
30 years	81,164.97
40 years	163,114.11

Look at what happens in the last decade. Between year 30 and year 40 the balance grows by 81,949 — more than the entire balance at year 30, and eight times the original 10,000. Nothing changed. The rate is the same, the money is the same. The balance is simply larger, so 7% of it is larger too.

That is the whole idea, and it is why time matters more than the amount.

The formula

A = P × (1 + r/n)^(n × t)

Symbol	Meaning
A	The final balance
P	The starting amount
r	The annual rate, as a decimal — 7% is 0.07
n	How many times a year interest is added
t	Years

A worked example

10,000 at 7%, compounded monthly, for 20 years.

1. Rate per period. 0.07 ÷ 12 = 0.0058333
2. Number of periods. 12 × 20 = 240
3. Growth factor. (1.0058333)²⁴⁰ = 4.038739
4. Balance. 10,000 × 4.038739 = 40,387.39

You earned 30,387.39 on 10,000, without doing anything.

How often interest is added matters — a little

10,000 at 6% for 10 years, changing only the compounding frequency:

Interest added	Balance after 10 years
Yearly	17,908.48
Every 6 months	18,061.11
Quarterly	18,140.18
Monthly	18,193.97
Daily	18,220.29

Daily beats yearly by 311.81 over a decade — real, but small. The frequency is worth checking when comparing two otherwise identical accounts, and is not worth chasing at the expense of a better rate.

Adding money every month changes the shape

Most people are not sitting on a lump sum; they are putting a little aside each month. Contributions and compounding work on each other.

10,000 to start, then 200 a month at 7% for 20 years:

• Paid in: 58,000
• Final balance: 144,572.72
• Interest earned: 86,572.72

The interest is larger than everything you put in. The calculator above marks the point where that crossover happens for your own numbers — the moment your money starts out-earning your saving.

Starting earlier beats saving more

Two people save 200 a month at 7%. One starts at 25 and stops at 65. The other starts at 35.

	Paid in	Ends with
40 years of saving	96,000	524,962.68
30 years of saving	72,000	243,994.20

Ten extra years of contributions cost 24,000 and produced 280,968 more. The extra money is not what did the work; the extra time is.

This is the single most useful thing on this page. If you are deciding between starting small now and starting properly later, start now.

How long until money doubles?

Annual return	Doubles in
5%	14.21 years
7%	10.24 years
10%	7.27 years
12%	6.12 years

These are exact figures — ln(2) ÷ ln(1 + r) — not the “rule of 72”, which is a mental shortcut that is close but never exact.

Two honest cautions

Inflation is not in these numbers. If your money grows 7% a year while prices rise 4%, your real gain is roughly 3%. A balance that looks life-changing in 30 years buys considerably less than the same figure buys today.

A steady return is an assumption, not a promise. Savings accounts pay a rate that changes. Investments do not return a smooth 7% — they return something different every year, sometimes negative. Compounding is arithmetic; the rate you put into it is a forecast.