- The compound interest formula uses just four variables: principal, rate, compounding frequency, and time.
- You do not need advanced maths skills to work out compound interest manually.
- Online calculators can do the heavy lifting, but understanding the formula helps you make sense of the results.
- The Rule of 72 gives you a quick mental shortcut for estimating how long it takes to double your money.
The Compound Interest Formula Explained in Plain English
Before we walk through the steps, here is the formula you will be using. Do not let it intimidate you. Once you know what each letter means, it all makes sense.
That is it. Five letters, one formula. Everything else is just plugging in your own numbers and doing the arithmetic.
How to Calculate Compound Interest in 5 Steps
We will use a worked example throughout: £2,000 deposited at 4% annual interest, compounded monthly, for 10 years.
Step 1: Identify Your Principal (P)
This is your starting deposit or investment. In our example, P = £2,000.
Step 2: Convert the Interest Rate to a Decimal (r)
Take the annual percentage rate and divide it by 100. An interest rate of 4% becomes 0.04. In our example, r = 0.04.
Step 3: Determine the Compounding Frequency (n)
This is how many times per year the interest is calculated and added. Monthly means n = 12. In our example, n = 12.
Step 4: Set the Time Period (t)
How many years will the money be left to grow? In our example, t = 10.
Step 5: Plug Everything Into the Formula
A = 2000 × (1 + 0.04/12)12×10. First, divide 0.04 by 12 to get 0.003333. Add 1 to get 1.003333. Raise this to the power of 120. The result is approximately 1.4908. Multiply by £2,000 and your final amount is approximately £2,981.67.
The Rule of 72: A Mental Shortcut Worth Knowing
If you want a quick estimate of how long it will take for your money to double, divide 72 by the annual interest rate.
How Compounding Frequency Changes the Result
The same interest rate produces different results depending on how often it compounds. Let us compare £10,000 at 5% over 10 years.
| Frequency | Per Year | After 10 Years | Total Interest |
|---|---|---|---|
| Annually | 1 | £16,289 | £6,289 |
| Quarterly | 4 | £16,436 | £6,436 |
| Monthly | 12 | £16,470 | £6,470 |
| Daily | 365 | £16,487 | £6,487 |
The gap between annual and monthly compounding is roughly £181 here, but it grows with larger balances and longer time periods.
Calculating With Regular Contributions
The basic formula assumes a single deposit. In practice, most savers add money regularly. The formula for future value with contributions is:
FV = P(1 + r/n)nt + PMT × [((1 + r/n)nt − 1) / (r/n)]
Where PMT is your regular contribution. For most people, an online calculator is the easiest way to work this out.
Benefits and Disadvantages of Calculating Yourself
Common Mistakes
Forgetting to Convert the Percentage
Using 5 instead of 0.05 gives absurdly large results. Always divide by 100.
Wrong Compounding Frequency
If your account compounds monthly but you calculate with annual, results will be off.
Ignoring Inflation
The formula gives nominal value. To estimate real returns, subtract expected inflation from the rate.
Overlooking Fees and Tax
Interest above your Personal Savings Allowance is taxable. The formula gives gross figures.