💰 Interest
Interest Calculator
Compare simple and compound interest for the same principal, rate and term, and see how much compounding frequency really adds. Press Calculate.
Simple vs compound interest
Simple interest is always calculated on the original principal, so it grows in a straight line. Compound interest is charged on the principal plus previously earned interest, so it curves upwards. Over long periods that curve makes a large difference.
- Simple: A = P × (1 + r × t)
- Compound: A = P × (1 + r ÷ n)n × t
- Continuous: A = P × er × t
- Effective annual rate = (1 + r ÷ n)n − 1
- Doubling time ≈ 72 ÷ annual rate (rule of 72)
Worked example
1,000 at 5% a year earns 150 in simple interest over three years. Compounded annually, the same amount grows to 1,000 × 1.05³, which is 1,157.63 — 157.63 of interest, 7.63 more than the simple version.
Everyday uses
- Comparing savings accounts and bonds
- Understanding what a loan really costs
- Seeing the difference between APR and APY
- Quick projections for a deposit
- Explaining why compounding accelerates over time
Fees, and why the effective rate is the honest one
Two loans can carry the same nominal interest rate and cost different amounts, because the fee structure is part of the price. Borrow 10,000 for a year at 5 percent with a 200 arrangement fee deducted up front: you receive 9,800 and repay 10,500. The interest is 500, but the cost of the money you actually received is 700 ÷ 9,800 = 7.14 percent. The headline 5 percent describes the rate, not the deal.
That gap is what APR exists to close. It folds the rate and most fees into one annualised number so two offers can be compared directly. Compare like with like, though: APR assumes the loan runs to term and every payment is made on time, so an APR comparison between a one-year loan and a five-year loan still needs the total cost alongside it.
The same logic applies to savings. An account advertising 4.00 percent compounded monthly pays an effective 4.074 percent over a year; compounded daily, 4.081 percent. The difference is small at these rates and grows with the rate. When a bank quotes an AER or effective annual rate, it has already done that arithmetic for you — and that is the number to use when comparing accounts.
Frequently asked questions
More worked examples
- 1,000 at 5% simple interest for 3 years earns 150.
- The same 1,000 compounded annually grows to 1,157.63 — interest of 157.63.
- Compounded monthly it reaches 1,161.47, slightly more again.
- By the rule of 72, money at 6% doubles in roughly 72 ÷ 6 = 12 years.
Effect of compounding frequency at 5%
| Compounding | Effective annual rate |
|---|---|
| Annually | 5.000% |
| Quarterly | 5.095% |
| Monthly | 5.116% |
| Daily | 5.127% |
| Nominal 12%, monthly | 12.683% |
Common mistakes to avoid
- Comparing an APY from one account with an APR from another — they are not the same measure.
- Forgetting that tax is charged on interest, so the return you keep is lower than the headline figure.
- Assuming a fixed nominal rate beats a variable one without checking how each has actually behaved.
- Using simple interest to describe a product that compounds.
Further questions
Assumptions and sources
Simple interest is calculated on the original principal only. Compound interest adds accrued interest to the balance at the chosen frequency. The comparison assumes a constant rate and no deposits, withdrawals or taxes.