Compound Interest: Simple Examples That Actually Click
Compound interest is “interest on interest”. Once you see a couple of quick examples, the idea sticks — and you’ll understand why starting early and paying in regularly beats chasing headline rates.
1) What is EAR/AER?
EAR (Effective Annual Rate) — or AER (Annual Equivalent Rate) for savings — tells you the true yearly return after compounding. If a bank quotes “5% compounded monthly”, the EAR is slightly higher than 5% because each month’s interest earns interest in later months.
Formula: EAR = (1 + r/m)m − 1, where r is the nominal annual rate and m is the compounding periods per year (12 for monthly).
2) Simple Example That Clicks
£1,000 at 5% nominal, monthly compounding (m=12)
- Monthly rate = 0.05 / 12 ≈ 0.4167%
- EAR = (1 + 0.05/12)12 − 1 ≈ 5.12%
- After 1 year: £1,000 × 1.0512 ≈ £1,051.20
If compounding were annual (m=1), you’d finish with exactly £1,050 — monthly compounding adds £1.20 extra.
3) Monthly vs Annual Compounding
More frequent compounding increases the effective return, but with diminishing impact above monthly/quarterly. At 5% nominal:
| Frequency | EAR / AER |
|---|---|
| Annual (m=1) | 5.00% |
| Quarterly (m=4) | 5.09% |
| Monthly (m=12) | 5.12% |
| Daily (m=365) | 5.13% |
It’s the difference between good and slightly better — the bigger gains come from time and regular contributions.
4) Why “Little and Often” Wins
Regular contributions let compounding work on every deposit. Starting earlier gives each pound more “time in the market.” Consider two savers paying the same total:
- Alice: £100/month for 10 years, then stops (total £12,000).
- Ben: Waits 10 years, then £200/month for 10 years (total £24,000).
Assuming 5% EAR, after 20 years Alice can be ahead of Ben despite contributing half as much — because her money had longer to compound. (Exact figures vary; try our Savings Growth Calculator.)
5) Rule of 72 (Back-of-the-Envelope)
A quick mental trick: divide 72 by the percentage return to estimate how many years to double your money. At ~6% EAR, it’s about 12 years; at 3%, ~24 years. It’s rough, but surprisingly handy.
6) Fees, Taxes, and Real Returns
Compounding works both ways: costs compound too. Account fees or platform charges reduce your effective rate, and taxes may apply to interest over your allowances. Focus on net (after-fee, after-tax) returns when comparing products.
7) Key Takeaways
- EAR/AER is the real, compounded yearly return.
- Compounding frequency matters, but time invested and regular deposits matter more.
- Start early, automate monthly contributions, and keep fees low.
- Use CalcFlow’s Savings Growth Calculator to model your own plan.