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Interest Calculator

What Is Compound Interest?

Compound interest is the interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest, which is calculated only on the principal, compound interest allows your money to grow exponentially over time. Albert Einstein reportedly called it the eighth wonder of the world. The key insight is that each compounding period adds interest not just on your original deposit, but also on all previously earned interest. This creates a snowball effect where growth accelerates over time. The more frequently interest compounds — daily versus annually, for example — the faster your investment grows, though the difference between very frequent compounding periods becomes marginal.

How Compound Interest Is Calculated

The compound interest formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate as a decimal, n is the number of compounding periods per year, and t is the time in years. For continuous compounding, the formula becomes A = Pe^(rt), using Euler's number. When regular contributions are included, the future value of an annuity formula is added: FV = PMT × [((1 + r/n)^(nt) - 1) / (r/n)]. For beginning-of-period contributions, this is multiplied by (1 + r/n). The effective annual rate (APY) is calculated as (1 + r/n)^n - 1, which shows the true annual return accounting for compounding frequency.

Frequently Asked Questions

What is the difference between compound interest and simple interest?

Simple interest is calculated only on the original principal amount. Compound interest is calculated on the principal plus all previously earned interest. Over time, compound interest earns significantly more because you earn interest on your interest. For example, $10,000 at 5% simple interest earns $500/year every year. With compound interest, you earn $500 the first year, then $525 the second year (5% of $10,500), and the amount keeps growing.

How does compounding frequency affect my returns?

More frequent compounding produces slightly higher returns. Daily compounding at 5% gives an effective annual rate (APY) of 5.127%, while annual compounding stays at exactly 5%. The difference is most noticeable at higher interest rates and over longer periods. However, the gap between daily and monthly compounding is quite small — about 0.01% difference at typical savings rates.

What is APY and how is it different from APR?

APR (Annual Percentage Rate) is the stated annual interest rate without accounting for compounding. APY (Annual Percentage Yield) is the effective annual rate that includes the effect of compounding. A 5% APR compounded monthly produces a 5.116% APY. Banks advertise APY on savings (higher number looks better) and APR on loans (lower number looks better). Always compare APY to APY for an accurate comparison.

Should I contribute at the beginning or end of the period?

Contributing at the beginning of each period (annuity due) earns more than contributing at the end (ordinary annuity) because each contribution has one extra compounding period. The difference is typically small for short timeframes but can add up over decades. For a $500/month contribution at 7% over 30 years, beginning-of-period adds roughly $25,000 more than end-of-period.

How does the Rule of 72 work?

The Rule of 72 is a quick way to estimate how long it takes to double your money. Divide 72 by the annual interest rate: at 6%, your money doubles in approximately 12 years (72 ÷ 6 = 12). At 8%, it takes about 9 years. At 3%, about 24 years. This rule is most accurate for rates between 6-10% and assumes compound interest with no additional contributions.

How do taxes affect compound interest growth?

Taxes on interest income reduce your effective return. If you earn 5% interest and pay 25% tax, your after-tax return is 3.75%. This impact compounds over time — over 20 years, the difference between pre-tax and after-tax returns can be substantial. Tax-advantaged accounts like IRAs, 401(k)s, and Roth accounts let interest compound tax-free or tax-deferred, significantly boosting long-term growth.