Simple vs Compound Interest: What's the Difference?
Simple interest is calculated only on the original principal: I = P × r × t. Compound interest is calculated on the principal plus all previously earned interest — so interest earns interest. Over long periods, compound interest produces dramatically larger returns (or costs) than simple interest. This is why Einstein allegedly called compound interest "the eighth wonder of the world" — though the quote is likely apocryphal.
The difference between simple and compound interest is the difference between linear and exponential growth. Simple interest adds a fixed amount each period. Compound interest adds a percentage of an ever-growing total — so the amount added increases each period. For savings, compound interest makes money grow faster than you might expect. For debt, compound interest makes it accumulate faster than most people realise. The practical implication: time is the most powerful factor in compound growth, which is why starting to save early matters so much and why letting high-interest debt persist is so costly.
Key Differences at a Glance
| Feature | Simple Interest | Compound Interest |
|---|---|---|
| Formula | I = P × r × t | A = P(1 + r/n)^(nt) |
| Interest calculated on | Principal only | Principal + accumulated interest |
| Growth type | Linear (straight line) | Exponential (curve) |
| Example: £1,000 at 10%/yr for 10 yrs | £1,000 in interest (total: £2,000) | £1,594 in interest (total: £2,594) |
| Frequency of compounding | N/A — calculated once per period | Annual, quarterly, monthly, daily, continuous |
| Common use | Short-term loans, car loans (sometimes), bonds | Savings accounts, mortgages, credit cards, investments |
| Beneficial for | Borrowers (lower cost over time) | Savers (higher returns over time) |
Simple Interest: The Linear Case
Simple interest is calculated using the formula I = P × r × t, where P is the principal (original amount), r is the annual interest rate (as a decimal), and t is time in years. If you invest £1,000 at 5% per year for 3 years, the interest is £1,000 × 0.05 × 3 = £150. The total is always £1,150 regardless of when during the 3 years you calculate it — because interest only accrues on the original principal, not on any interest already earned. Simple interest is straightforward to calculate and is used for some short-term loans and bonds. In practice, most financial instruments use compound interest.
Compound Interest: The Exponential Force
Compound interest adds interest to the principal at each compounding period, and then calculates the next period's interest on the new, larger balance. The formula is A = P(1 + r/n)^(nt), where n is the number of compounding periods per year. With monthly compounding at 5% annual rate on £1,000 over 10 years: A = £1,000 × (1 + 0.05/12)^(12×10) = £1,647. The same calculation with annual compounding gives £1,629 — monthly compounding produces slightly more. More frequent compounding always produces higher returns. In the limit of continuous compounding, A = Pe^(rt) — exponential growth by the mathematical constant e.
The Rule of 72
A practical shortcut for understanding compound growth is the Rule of 72: divide 72 by the annual interest rate to get the approximate number of years for an investment to double. At 6% annual return, money doubles in approximately 72/6 = 12 years. At 10%, it doubles in 7.2 years. The rule works because ln(2) ≈ 0.693, and 72 ≈ 69.3 is a convenient approximation. Crucially, each doubling starts from the new, higher base — so after two doublings at 10% (about 14 years), £1,000 becomes £4,000; after three doublings (~21 years), £8,000. The compounding accelerates because each new doubling starts from a larger base.
Frequently Asked Questions
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal (I = Prt). Compound interest is calculated on the principal plus previously earned interest, causing the balance to grow exponentially. £1,000 at 10% for 10 years gives £1,000 in simple interest (total £2,000) but £1,594 in compound interest (total £2,594).
Is compound interest good or bad?
It depends on which side you're on. For savers and investors, compound interest is beneficial — it makes wealth grow faster the longer you leave it. For borrowers (credit cards, mortgages, student loans), compound interest means debt grows faster the longer it remains unpaid. The same mechanism that makes savings grow works against you on debt.
What is the Rule of 72?
The Rule of 72 is a shortcut: divide 72 by the annual interest rate to estimate how many years it takes for an investment to double. At 6%, money doubles in 72/6 = 12 years. At 10%, in about 7.2 years. It's an approximation (exact for ~8%) but accurate within 1% for rates between 6% and 10%.
What does "compounding frequency" mean?
Compounding frequency is how often interest is calculated and added to the principal — annually, quarterly (4x/year), monthly (12x), daily (365x), or continuously. More frequent compounding produces slightly higher effective returns. A 10% annual rate compounded monthly gives an effective annual rate of about 10.47%; compounded daily gives about 10.52%.
How We Write These Comparisons
SmartAss Facts comparisons are written to be the clearest, most accurate answer to "what is the difference between X and Y?" on the internet. We start from the primary definition — taxonomic, scientific, or linguistic — and work outward to the practical distinctions most people actually need.
Each comparison table row is independently sourced. If a distinction is more nuanced than a table cell allows, the detail appears in the body sections below the table. Last reviewed: 2026-05-25.
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