Understanding Compound Interest: Frequency, EAR, and Real Returns
Compound interest is the process by which interest earns interest on itself. The more frequently compounding occurs, the higher your effective return — even if the stated rate is identical. A 5% annual rate compounded monthly is worth more than 5% compounded annually. This guide explains the formula, the frequency effect, and the difference between what your account says it pays and what you actually earn.
The Compound Interest Formula
A = P × (1 + r/n)^(n×t) Where: A = Final amount P = Principal (initial deposit) r = Annual interest rate (decimal) n = Compounding periods per year t = Time in years
How Compounding Frequency Affects Returns
£10,000 at 5% annual rate over 10 years, different compounding periods:
| Frequency | n | Final Amount | Extra vs Annual |
|---|---|---|---|
| Annual | 1 | £16,289 | — |
| Quarterly | 4 | £16,436 | +£147 |
| Monthly | 12 | £16,470 | +£181 |
| Daily | 365 | £16,487 | +£198 |
| Continuous | ∞ | £16,487 | +£198 |
The difference between annual and daily compounding is modest (about 1.2% extra). The real impact of frequency becomes visible over longer periods and at higher rates.
Nominal vs Effective Annual Rate (EAR)
EAR = (1 + r/n)^n − 1 Example: 6% nominal rate, monthly compounding EAR = (1 + 0.06/12)^12 − 1 = 6.168% This is what you actually earn, not the stated 6%.
| Nominal Rate | Annual | Quarterly | Monthly | Daily |
|---|---|---|---|---|
| 3% | 3.000% | 3.034% | 3.042% | 3.045% |
| 5% | 5.000% | 5.095% | 5.116% | 5.127% |
| 8% | 8.000% | 8.243% | 8.300% | 8.328% |
| 12% | 12.000% | 12.551% | 12.683% | 12.747% |
What-If Scenarios
Scenario 1: Early vs late start — the decade of compounding
Both invest £300/month at 7% annual return until age 67:
| Start Age | Total Contributions | Final Amount |
|---|---|---|
| 22 | £162,000 | £875,000 |
| 32 | £126,000 | £454,000 |
| 42 | £90,000 | £220,000 |
Starting 10 years earlier nearly doubles the outcome despite only £36,000 more in contributions.
Scenario 2: The Rule of 72
A quick mental shortcut: divide 72 by the annual return to find doubling time.
| Annual Return | Years to Double |
|---|---|
| 3% | 24 years |
| 6% | 12 years |
| 9% | 8 years |
| 12% | 6 years |
Scenario 3: Compound interest working against you — credit card debt
£5,000 credit card balance at 24.9% APR, minimum payments only (~£100/month): Takes approximately 8 years to repay. Total interest paid: ~£4,600 — nearly as much as the original debt. Same balance paid at £300/month: repaid in under 2 years, total interest ~£1,100.
Frequently Asked Questions
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Indicative only. Investment returns are variable and not guaranteed. Past performance is not a guide to future results.