Compound Interest Guide
How compound interest works, why it beats simple interest, and how compounding frequency changes your savings.
The Core Idea
Simple interest: earn interest on your principal only. Compound interest: earn interest on your principal + all previously earned interest.
Formula: A = P × (1 + r/n)^(n×t) — where n is compounds per year. The more frequent n, the higher A.
Simple vs Compound Interest — Real Numbers
Starting with $10,000 at 5% — how the gap widens over time:
| Year | Simple Interest | Compound (monthly) | Compound Advantage |
|---|---|---|---|
| Year 1 | $10,500 | $10,512 | +$12 |
| Year 2 | $11,000 | $11,049 | +$49 |
| Year 5 | $12,500 | $12,834 | +$334 |
| Year 10 | $15,000 | $16,470 | +$1,470 |
| Year 15 | $17,500 | $21,137 | +$3,637 |
| Year 20 | $20,000 | $27,126 | +$7,126 |
| Year 30 | $25,000 | $44,677 | +$19,677 |
How Compounding Frequency Affects $10,000
At 5% nominal annual rate — daily vs monthly vs quarterly vs annually:
| Compounding | 5 yr | 10 yr | 15 yr | 20 yr | 30 yr |
|---|---|---|---|---|---|
| Annually | $12,763 | $16,289 | $20,789 | $26,533 | $43,219 |
| Quarterly | $12,820 | $16,436 | $21,072 | $27,015 | $44,402 |
| Monthly | $12,834 | $16,470 | $21,137 | $27,126 | $44,677 |
| Daily | $12,840 | $16,487 | $21,169 | $27,181 | $44,812 |
| Daily vs Annual gap | $77 | $198 | $380 | $648 | $1,593 |
* Daily compounding advantage is real but modest — rate differences between accounts matter far more than frequency.
Compound Interest on $5,000 Over 15 Years
Monthly compounding — interest earned shown in green:
Rate Matters More Than Frequency
On $10,000 over 10 years — a 0.5% rate increase beats the daily vs monthly compounding difference every time:
| Account Option | Rate | Frequency | After 10 years |
|---|---|---|---|
| Bank A — high rate | 5% | Monthly | $16,470 |
| Bank B — same rate, daily | 5% | Daily | $16,487 |
| Bank C — lower rate, daily | 4.5% | Daily | $15,683 |
| Bank D — lower rate, monthly | 4.5% | Monthly | $15,670 |