How Is Compound Interest Calculated?

Compound interest is calculated by growing the balance by the same percentage once for every period, so each period’s interest is earned on everything before it. The formula is A = P × (1 + r ÷ n)^(n × t), and £5,000 at 6% compounded monthly for six years comes to £7,160.22, of which £2,160.22 is interest.

This guide works that example through by hand, then shows what changes when you compound more often, add regular deposits or leave the money for longer.

What is the compound interest formula?

The US Consumer Financial Protection Bureau puts it plainly: compound interest is when you earn interest on the money you’ve saved and on the interest you earn along the way. In a formula (see also compound interest in the glossary):

A = P × (1 + r ÷ n)^(n × t)

• A is the final amount, including interest.
• P is the principal: the amount you start with.
• r is the annual interest rate as a decimal, so 6% is 0.06.
• n is how many times a year interest is added: 12 for monthly, 4 for quarterly, 1 for yearly.
• t is the number of years.

The part in brackets is the growth factor for one period. Raising it to the power n × t applies it once for every period in the whole term.

A worked example: £5,000 at 6% for six years

Here is the sum with monthly compounding.

1. Find the rate per period. 6% a year is 0.06, and 0.06 ÷ 12 = 0.005 a month.
2. Count the periods. 12 months × 6 years = 72.
3. Work out the growth factor. 1 + 0.005 = 1.005, and 1.005 raised to the power 72 is about 1.4320.
4. Multiply by the principal. £5,000 × 1.4320 = £7,160.22.
5. Take the principal away to isolate the interest: £7,160.22 − £5,000 = £2,160.22.

You can see the “interest on interest” in the first few steps. Month one earns £5,000 × 0.005 = £25.00. Month two earns 0.5% of £5,025, which is about £25.13, because the first month’s £25 is now earning interest too.

Year by year, the interest grows even though the rate never changes:

Year six earns £107.58 more than year one on exactly the same 6% rate. That growing gap is the whole point of compounding.

Try it with your own numbers

The calculator below opens with the same £5,000, 6% a year, monthly compounding and six years, so you will see £7,160.22 as the future value, £2,160.22 in interest and an effective annual rate of 6.17%. Change the rate, the term or the compounding frequency and watch the interest column move.

How is compound interest different from simple interest?

Simple interest is worked out on the original amount only: principal × rate × years. For £5,000 at 6% over six years that is £5,000 × 0.06 × 6 = £1,800, a final balance of £6,800.

Compounding adds £360.22 on top of that over the same six years, and the gap grows with time:

After 20 years the compounded balance has earned £11,551.02 in interest against £6,000 for simple interest. Nothing about the rate changed. The extra is interest earned on earlier interest.

Does compounding more often make a big difference?

It helps, but less than most people expect. Here is the same £5,000 at 6% over six years, changing only how often interest is added:

Daily compounding here uses a 365-day year. Going from yearly to monthly adds £67.62; going from monthly to daily adds only another £6.22. The gains shrink at each step, and even continuous compounding, the theoretical limit, only reaches £7,166.65.

How do you calculate compound interest with regular deposits?

Most people are not investing a single lump sum. When you add the same amount each month, treat the starting amount and the deposits as two separate pots that both grow:

total = P × (1 + i)^n + deposit × ((1 + i)^n − 1) ÷ i

Here i is the rate per period (0.005 for 6% a year paid monthly) and n is the number of deposits (72). With £5,000 to start and £100 added at the end of each month:

• The starting £5,000 grows to £7,160.22, as before.
• The 72 deposits are worth £100 × (1.4320 − 1) ÷ 0.005 = about £8,640.89.
• Together that is £15,801.11, of which £12,200 is money you paid in and £3,601.11 is interest.

In the calculator, choose deposits, enter £100 a month and leave the timing on the end of the month to reproduce this. Deposits made at the start of each month earn slightly more, because each one has an extra month to grow. The calculator lets you switch that timing.

Why does time matter more than the rate?

Because the growth factor is raised to a power. Each extra year multiplies the balance again, so the early years do little and the later years do a lot. On £5,000 at 6%, the first ten years add £4,096.98. The next ten add £7,454.04 (from £9,096.98 to £16,551.02), nearly twice as much from the same rate.

The practical consequence is that starting earlier, or leaving money untouched for longer, usually beats finding a slightly higher rate.

Does compounding work against you on debt?

Yes. The same maths applies to money you owe. If interest is added to a balance you carry and you only pay part of it, the next charge is calculated on a larger figure. That is why a balance you leave on a credit card keeps costing more, and why the repayments on a mortgage or loan are front-loaded with interest, as explained in how a mortgage repayment is calculated.

Before putting money into long-term investments, it is worth having a cash cushion that you will not need to withdraw early. The emergency fund calculator shows how big that cushion should be and how long it takes to build.

What mistakes should you avoid?

• Using the annual rate for monthly periods. Divide the annual rate by n and multiply the years by n. Using 6% with 72 periods gives a wildly wrong answer.
• Typing 6 instead of 0.06. In the formula the rate is a decimal. In the calculator you enter 6.
• Treating the result as a promise. The formula assumes a constant rate. Savings rates change and investment returns vary from year to year, so the answer is an illustration, not a forecast. It also ignores tax, fees and inflation.
• Mixing up deposit timing. Deposits at the start of each period grow for one extra period compared with deposits at the end.

What to do next

Enter your own starting amount, rate and term in the compound interest calculator, add a monthly deposit, and compare yearly against monthly compounding to see how much the frequency really matters for your figures. The year-by-year table shows exactly how much of each year’s growth is interest on interest.

Sources: Consumer Financial Protection Bureau: How does compound interest work?, FDIC: Money Smart, Chapter 5, Compound interest.

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