How to Calculate Compound Interest: Formula, Steps, and Worked Examples

The compound interest formula looks more complicated than it is. Once you've worked through one example manually, the logic becomes intuitive — and you'll be able to estimate outcomes in your head without needing a tool.

The Formula

Step-by-Step Calculation

Let's work through an example: €5,000 invested at 6% annual interest, compounded monthly, for 10 years.

1. Identify variables:
   • P = €5,000
   • r = 0.06 (6% as decimal)
   • n = 12 (monthly compounding)
   • t = 10
2. Calculate r/n: 0.06 / 12 = 0.005 (monthly interest rate)
3. Calculate n × t: 12 × 10 = 120 (total compounding periods)
4. Calculate (1 + r/n)^(n×t): (1.005)^120 = 1.8194
5. Multiply by P: €5,000 × 1.8194 = €9,097
6. Interest earned: €9,097 − €5,000 = €4,097

Your €5,000 grew to €9,097 over 10 years — nearly doubling — with €4,097 in interest earned on top of the original principal.

Compounding Frequency: How It Affects the Result

The same €5,000 at 6% over 10 years with different compounding frequencies:

More frequent compounding earns more interest, but the differences are modest. Monthly vs. annual compounding on €5,000 over 10 years adds just €143. Over €100,000 for 30 years, the differences become more significant — but still a second-order effect compared to the rate and time horizon.

Adding Regular Monthly Contributions

Most real-world savings involve regular contributions, not just a lump sum. The formula extends to include a monthly payment (PMT):

The second term calculates the future value of your regular contributions stream. This formula is what's behind every pension, ISA, and retirement account projection.

Worked Example: Lump Sum + Monthly Contributions

€5,000 initial investment + €200/month at 6% for 10 years:

• Lump sum component: €9,097 (as above)
• Monthly contribution component: €200 × [(1.005)^120 − 1] / 0.005 = €200 × 163.88 = €32,776
• Total: €9,097 + €32,776 = €41,873
• Total contributed: €5,000 + (€200 × 120 months) = €29,000
• Interest earned: €41,873 − €29,000 = €12,873

The Rule of 72: Mental Maths Shortcut

For quick estimates of doubling time, divide 72 by the annual interest rate:

• At 4%: doubles in ~18 years
• At 6%: doubles in ~12 years
• At 8%: doubles in ~9 years
• At 10%: doubles in ~7.2 years

This works because ln(2) ÷ ln(1 + r) ≈ 0.693 / r, and 72 is a convenient approximation of 69.3 that divides cleanly by many common interest rates.

Continuous Compounding: The Theoretical Maximum

When interest compounds continuously (n → infinity), the formula simplifies to:

For our €5,000 example: A = €5,000 × e^(0.06 × 10) = €5,000 × 1.8221 = €9,110. Very close to daily compounding — the practical limit is already nearly reached at monthly.