How to Calculate Compound Interest by Hand (Step by Step)
Grasping the compound interest formula once means you'll never fall for the misleading headline numbers banks quote. Here is every step, by hand, with a pound example you can verify on a basic calculator.
The formula
A = P × (1 + r/n)^(n × t)
Where each letter represents:
- A — the final amount (what you end up with)
- P — principal, your starting amount
- r — annual interest rate as a decimal (so 7% = 0.07)
- n — number of compounding periods per year (monthly = 12, annually = 1)
- t — number of years
Worked example: £1,000 at 7% compounded annually for 30 years
Plug the variables into the formula:
- P = 1000
- r = 0.07
- n = 1 (annual compounding)
- t = 30
So we get:
A = 1000 × (1 + 0.07/1)^(1 × 30)
A = 1000 × (1.07)^30
Now raise 1.07 to the power of 30. On a calculator:
1.07^30 ≈ 7.6123
So:
A = 1000 × 7.6123 ≈ £7,612
That's right — £1,000 becomes £7,612 over 30 years with no further contributions. £6,612 of that is interest, much of it earned on interest that was previously added. That's compounding.
Verify these numbers on the calculator →
Step-by-step on any calculator
- Divide the annual rate by the number of periods (compounding frequency):
0.07 ÷ 1 = 0.07 - Add 1:
0.07 + 1 = 1.07 - Multiply the years by the periods per year:
30 × 1 = 30 - Raise the result from step 2 to the power from step 3:
1.07^30 ≈ 7.6123(use thex^yory^xkey, or type1.07, thenPOWERor^, then30, then=) - Multiply by the principal:
7.6123 × 1000 = 7612.3
That's it. The result is your final amount. Subtract the principal if you want just the interest portion: 7612.3 − 1000 = £6,612 of interest.
Why monthly compounding changes the result
If the same £1,000 at 7% instead compounds monthly (n = 12):
A = 1000 × (1 + 0.07/12)^(12 × 30)
A = 1000 × (1.005833)^360
A ≈ £8,116
Monthly compounding produces £8,116 instead of £7,612 — about £500 (7%) more over 30 years. The more frequently interest is added, the more it can compound. This is why banks sometimes quote two different rates: the nominal rate (the headline) and the effective annual rate (what you actually get, given the compounding frequency).
Adding regular contributions
The formula above only handles a single lump sum. With monthly contributions, each contribution starts compounding at a different time, so you have to compute period by period — which is what a calculator does for you. The intuition: every pound you add earns interest from the moment it goes in, so earlier contributions matter more than later ones.
For a feel, £1,000 plus £200 a month at 7% over 30 years becomes roughly £268,000 — a vastly different numberbecause each £200 contribution compounds for as long as it remains invested. Run your own scenario on the compound interest calculator and watch the year-by-year growth in the schedule.
Frequently asked questions
What is the compound interest formula?
A = P × (1 + r/n)^(n×t), where A is the final amount, P is the principal, r is the annual rate as a decimal, n is the number of compounding periods per year, and t is the number of years.
How is compound interest different from simple interest?
Simple interest only earns interest on your original principal. Compound interest earns interest on both the principal and the interest that has already been added, so your money grows faster the longer it stays invested.
What is a good example of compound interest?
£1,000 invested at 7% for 30 years becomes £7,612 with no further contributions — over 7 times your original investment, with £6,612 of that being interest earned on interest.
Bottom line
The formula isn't hard once you've done it once. The hard part is internalising what the answer means: that a 30-year disciplined habit with small amounts will outperform a 5-year attempt with large amounts and an early exit. Use the compound interest calculator to model longer scenarios without manually raising 1.07 to the power of 30 twice.