Interest Calculator
Calculate simple and compound interest with step-by-step formulas, worked examples, and clear explanations of nominal vs. effective rates.
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How to use
Enter a principal amount, annual interest rate, and time period to calculate interest earned. Simple interest applies the rate to the original principal only. Compound interest applies the rate to the growing balance, resulting in faster growth over time. Use the tabs above to switch between the two modes.
How simple interest works
Simple interest is calculated only on the original amount you deposit or borrow (the principal). The formula is: I = P × r × t, where I is the interest earned, P is the principal, r is the annual interest rate expressed as a decimal, and t is the time in years.
Worked example: you deposit $1,000 at a 10% annual simple interest rate for 2 years. The calculation is I = 1,000 × 0.10 × 2 = $200. At the end of the 2 years you have $1,200. Notice that the interest earned in year 1 ($100) does not itself earn interest in year 2 — that is the defining feature of simple interest.
Simple interest is common in short-term personal loans, some car loans, and informal lending. It is easy to verify by hand, which makes it useful for checking whether a lender's numbers add up.
How compound interest works
Compound interest is calculated on the principal plus all previously accumulated interest. The formula is: A = P × (1 + r/n)^(n×t), where A is the final amount, P is the principal, r is the annual rate as a decimal, n is the number of times interest compounds per year, and t is the time in years.
Worked example: the same $1,000 at 10% annual interest for 2 years, compounded annually (n = 1). Year 1: 1,000 × 1.10 = $1,100. Year 2: 1,100 × 1.10 = $1,210. Total interest: $210 — that is $10 more than simple interest, because the $100 earned in year 1 also earned 10% in year 2. Over longer periods this gap grows dramatically: the same deposit over 20 years yields $2,000 in simple interest but $5,727 in compound interest.
Compounding frequency matters. At the same nominal rate, monthly compounding produces more than annual compounding. $1,000 at 10% for 2 years compounded monthly gives A = 1,000 × (1 + 0.10/12)^24 ≈ $1,220.39 — slightly more than the $1,210 from annual compounding.
Nominal vs. effective rate: the most common mistake
A rate advertised as '2% monthly' is not the same as 24% per year. Because of compounding, the effective annual rate is (1.02)^12 − 1 = 26.82%. This difference is the single most common source of confusion in loans and credit cards, and it always works against the borrower who assumes simple multiplication.
The same applies in reverse: a '12% annual rate, compounded monthly' means 1% is applied each month, and the effective annual rate is (1.01)^12 − 1 = 12.68%, not 12%. When comparing loan or investment offers, always compare effective annual rates — never mix a monthly rate from one offer with an annual rate from another.
Rule of thumb: to convert a monthly rate to its effective annual equivalent, use (1 + monthly rate)^12 − 1. To go from an annual nominal rate compounded monthly to the effective rate, divide by 12 first, then apply the same formula — or let our effective interest rate calculator do the conversion for any compounding frequency.
The rule of 72: quick mental math
To estimate how many years it takes for money to double at a given compound rate, divide 72 by the annual rate. At 8% per year, money doubles in roughly 72 ÷ 8 = 9 years. At 12%, roughly 6 years. This approximation works well for rates between 4% and 15% and is useful for quickly evaluating whether an investment claim is plausible.
It also works in reverse for debt: a credit card charging an effective 36% annual rate doubles what you owe in about 2 years if you make no payments. Seeing debt through the rule of 72 makes the real cost of high-interest borrowing much more tangible. To see the exact month-by-month cost of a loan, use our loan calculator and its amortization table.
Frequently Asked Questions
What is the difference between simple and compound interest?
Simple interest is calculated only on the principal, so it grows linearly. Compound interest is calculated on the principal plus accumulated interest, so it grows exponentially. Over short periods the difference is small; over decades it is enormous.
How often is interest compounded?
It depends on the product: savings accounts often compound monthly or daily, certificates of deposit typically monthly or at maturity, and loans usually monthly. The more frequently interest compounds, the more you earn on savings — or owe on debt — at the same nominal rate.
Is a 2% monthly rate the same as 24% per year?
No. Because of compounding, 2% monthly is an effective 26.82% per year: (1.02)^12 − 1 = 0.2682. Multiplying a monthly rate by 12 gives the nominal rate, which understates the true annual cost.
What is APR and how is it different from the interest rate?
APR (Annual Percentage Rate) is the yearly cost of borrowing including fees and commissions, while the interest rate reflects only the cost of the money itself. Two loans with the same interest rate can have very different APRs if one charges higher fees.
Which is better for savings: a higher rate or more frequent compounding?
The rate matters much more. Going from annual to monthly compounding at 10% adds only about 0.47 percentage points of effective yield, while going from 10% to 11% adds a full point. Compare effective annual rates to see the true difference.
Does this calculator work for loans as well as savings?
Yes. The math is identical — for savings, the interest is what you earn; for loans, it is what you pay. Note that most amortizing loans (like mortgages) use a payment schedule where each installment covers interest plus part of the principal, which requires an amortization calculation rather than a lump-sum one.