Compound interest explained (in plain English)

Compound interest is the idea that your money can grow in layers. In the beginning, interest feels small because you’re earning interest on a small balance. But as your balance grows, the same percentage rate produces bigger dollar amounts. Over long time periods, the growth can look “exponential” — not because the rate changes, but because the base you’re applying it to keeps getting larger.

Simple interest pays interest only on the original principal. If you invest $10,000 at 5% simple interest, you earn $500 per year (assuming the rate doesn’t change). After 10 years, you’d earn $5,000 total interest and end with $15,000. It grows in a straight line.

Compound interest reinvests interest into the balance, so you earn interest on the original principal and on previously earned interest. If the same $10,000 earns 5% compounded annually, after year 1 you have $10,500. After year 2 you earn 5% on $10,500, not $10,000 — so you gain $525. That little extra keeps stacking.

The “secret sauce” is time. Compounding is like rolling a snowball: the longer you roll it, the more snow it collects — and the faster it grows. This is why long-term investing, retirement accounts, and even high-yield savings accounts often talk about compounding frequency and annual return.

When interest compounds more frequently (monthly or daily), your balance gets updated more often. That means interest starts earning interest sooner. The difference between monthly vs daily compounding is usually small compared to the difference between “invested for 5 years” vs “invested for 25 years.” But when balances get large and time gets long, frequency can add up.

Regular deposits are often more powerful than trying to guess the “perfect” rate. Contributing $200/month consistently can beat a higher-risk plan that adds nothing. Contributions also change your intuition: the final balance includes both your deposits and the interest on those deposits. This calculator separates those so you can see what you put in versus what you earned.

Compound interest formulas used

This calculator uses the standard compound interest model and an annuity model for regular monthly contributions. Here are the core formulas (in readable form).

If you invest a starting amount P at an annual rate r (as a decimal) for t years, compounded n times per year:

FV = P × (1 + r/n)^(n×t)

If you contribute PMT each month and interest compounds monthly, a simplified model is:

FV_contrib = PMT × [((1 + i)^m − 1) / i]

where i is the monthly rate and m is the number of months. If contributions happen at the beginning of the month (deposit first), we multiply by (1+i).

In real life, compounding schedules and deposit schedules can differ. To keep this tool accurate across common compounding options (annual/quarterly/monthly/daily), we simulate the balance over time using small time steps based on the compounding frequency. Deposits are applied monthly, and interest accrues per compounding period.

APY (effective annual yield) converts compounding frequency into an equivalent “once per year” return: APY = (1 + r/n)^n − 1

This is not the same as market returns, but it’s useful for comparing savings accounts or CDs.

Compound interest examples (with real numbers)

Starting amount $5,000, annual rate 7%, time 10 years, compounded monthly.

The monthly rate is approximately 0.07/12. After 10 years, your balance is roughly: $9,900–$10,100 (depending on rounding). The “earned” portion is about $4,900–$5,100.

Same as above, but with a regular contribution of $200/month. Now you contribute $200 × 120 months = $24,000 over the decade, plus the initial $5,000. Total contributed cash is $29,000.

With compounding, you might end around $44,000–$47,000. The difference (about $15,000–$18,000) is your estimated interest earned — money that came from growth rather than deposits.

Keep the same $200/month and 7%, but compare 10 years vs 30 years. The first decade is mostly “building the base.” The later decades are where interest on interest becomes dominant. Many people find that the 20–30 year range creates a result that feels dramatically larger than expected.

Frequently Asked Questions

• What’s the difference between APR and APY?

  APR is the nominal annual rate (often quoted by banks). APY includes the effect of compounding frequency. If interest compounds monthly, the APY is slightly higher than the APR.

• Does compounding daily vs monthly make a big difference?

  Usually it’s a small difference compared to time and contribution size. Daily compounding can add a bit more growth, but adding years (or adding deposits) often matters more.

• How should I pick an “expected rate” for investing?

  Many people test a range (like 4%, 6%, 8%) to model conservative vs optimistic scenarios. For diversified long-term portfolios, historical averages are often discussed in that range, but nothing is guaranteed.

• Why do my results differ from my brokerage calculator?

  Different tools may assume different deposit timing, different compounding schedules, and may include fees or taxes. This calculator keeps assumptions simple and transparent.

• Can I use this for loan interest too?

  You can approximate, but loans often have payments that reduce principal, and interest may be calculated differently. For loans, use an amortization or EMI calculator.

• What if the interest rate changes over time?

  This calculator assumes a constant rate. If your rate changes, run separate scenarios for each period or use an average rate for a planning estimate.