The Power of Compound Interest: Your Complete Guide
Albert Einstein allegedly called compound interest "the eighth wonder of the world." Whether or not he actually said it, the sentiment is mathematically sound: given enough time, money invested at even modest interest rates grows dramatically. This calculator shows you exactly how powerful that effect is for your specific situation.
How Compound Interest Works
Unlike simple interest (which only earns interest on your original principal), compound interest earns interest on both your principal and the interest already accumulated. The formula is:
A = P(1 + r/n)nt + PMT × [(1 + r/n)nt − 1] / (r/n)
Where P = principal, r = annual rate, n = compounding periods per year, t = years, PMT = monthly payment.
The Rule of 72
The Rule of 72 is a simple mental shortcut to estimate how long it takes money to double: divide 72 by the annual interest rate. At 6% annual return, your money doubles roughly every 12 years. At 8%, every 9 years. At 10%, every 7.2 years.
This rule explains why starting early makes such a dramatic difference. Someone who invests $5,000/year from age 25–35 (just 10 years) and then stops often ends up with more at 65 than someone who invests $5,000/year from age 35–65 (30 years) — the first decade of compound growth is that powerful.
Where to Save: Interest Rate Benchmarks (2024)
- Standard savings account: 0.01–0.5% — barely keeps up with fees
- High-yield savings (HYSA): 4–5.5% — best for emergency funds and short-term goals
- Money market accounts: 4–5.2% — similar to HYSA, some restrictions
- US Treasury bonds (I-bonds): 4–6% — inflation-protected, capped at $10k/year
- Index funds (S&P 500 historical): ~10% nominal, ~7% real — best for 10+ year horizons
- Target-date retirement funds: 6–8% expected — diversified, automatically rebalances
Savings Goal Benchmarks
Financial planners use several rules of thumb for savings targets:
- Emergency fund: 3–6 months of expenses in liquid savings
- House deposit: 10–20% of home value (plus 2–5% for closing costs)
- Retirement: 25× your annual expenses (the "4% rule") — so $50k/year lifestyle needs $1.25M saved
- By age 30: ~1× your annual salary saved for retirement
- By age 40: ~3× annual salary
- By age 50: ~6× annual salary
Tips to Grow Your Savings Faster
- Automate contributions: Set up automatic transfers on payday so you never have to decide whether to save
- Increase rate by 1% each year: Small annual increases, timed with raises, compound dramatically over decades
- Use tax-advantaged accounts first: Max out your 401(k) match, then ISA/IRA, before taxable accounts
- Reinvest all dividends: Turn off the option to receive dividends as cash — reinvesting them supercharges compounding
- Avoid withdrawals before retirement: Early withdrawal penalties and lost compounding time are devastating to long-term growth
Frequently Asked Questions
What's the difference between APR and APY? APR (Annual Percentage Rate) is the base interest rate. APY (Annual Percentage Yield) accounts for compounding — it's always equal to or higher than APR. When comparing savings accounts, use APY; when comparing loans, use APR.
How often does compound interest compound? Most savings accounts compound daily, which gives slightly better returns than monthly compounding. Our calculator assumes monthly compounding, which is the most common basis for comparisons.
Is my money safe in a high-yield savings account? Yes — all FDIC-insured (US) or FSCS-insured (UK) accounts protect your savings up to regulatory limits regardless of whether the bank fails.
What if inflation reduces my real return? With inflation around 3%, a 5% APY account delivers roughly 2% in real purchasing power. Long-term inflation-beating growth generally requires equities (stocks), not savings accounts.
When should I prioritise savings vs paying off debt? If your debt interest rate exceeds your expected savings return, pay off debt first. Credit cards (15–25%) should almost always be cleared before adding to savings.