Math

Interest Calculator

Two interest models, very different math: <strong>simple interest</strong> (interest only on the original principal — used in some short-term loans, mortgages computed differently) and <strong>compound interest</strong> (interest on interest, the standard for savings, investments, and most loans). This calculator runs both. Add a monthly contribution to model a savings habit that's growing on top of compounding returns. Over long horizons, compound interest with regular contributions is the math behind retirement — starting at 25 with $200/month at 7% returns gets you to $525,000 by 65; starting at 45 gets you to $100,000.

Simple vs compound interest

Simple interest: A = P + (P × r × t). Interest is calculated only on the original principal. After 20 years at 7%, $10K grows to $10K + ($10K × 0.07 × 20) = $24K. Mostly used in short-term loans (auto loans, some personal loans) and educational examples.

Compound interest: A = P × (1 + r/n)^(n×t). Interest accumulates on previously-earned interest. Same $10K at 7% compounded monthly for 20 years = $40,387 — nearly 70% more than simple interest. The difference grows exponentially with time.

Worked example: $10K at 7% for 20 years with $200/month contributions, compounded monthly. Initial $10K grows to $40,387. Monthly $200 contributions over 20 years ($48K contributed) grows to $104,113. Total = $144,500. Of that, you contributed $58K and earned $86,500 in interest.

The Rule of 72

Approximate years to double money = 72 / annual rate %. Useful for mental math.

1% (big-bank savings): 72 years to double
4% (HYSA, bonds): 18 years
6% (mixed portfolio): 12 years
7% (long-term stocks after inflation): 10.3 years
10% (long-term US stocks nominal): 7.2 years
12% (aggressive growth): 6 years

How to use this calculator

Pick mode: Compound (most savings/investments) or Simple.
Starting amount: initial deposit.
Annual rate: nominal expected return.
Years: time horizon.
Monthly contribution: optional recurring deposit.
Compounding: monthly is most accounts; daily slightly more; annual slightly less.
Output: final balance, total contributed, interest earned.

Common scenarios

$10K invested today at 7%, 30 years, no contributions. Simple: $31K. Compound: $76K. The compounding advantage on a single lump sum: $45K more.

$500/month contributions only (no starting balance) at 8%, 40 years. $1.75 million. You contributed $240K. Interest of $1.5M is from compounding. The retirement savings argument made tangible.

$25K starting at 5%, $0 contributions, 10 years. Compound: $41K. Simple: $37.5K. Decent growth for emergency-fund-or-bond money at modest rates.

FAQ

Simple vs compound — which one am I using? +

For almost everything: compound. Savings accounts, investment accounts, credit cards (compound against you), most mortgages, retirement accounts. Simple interest mostly appears in short-term auto loans, some personal loans, and as a textbook example. If your money is in a bank, brokerage, or 401k, it's compound.

What's a realistic rate? +

HYSA / bonds: 4-5% (2024-2025 rates). Long-term US stocks (S&P 500): 10% nominal (~7% real after inflation). Real estate: 8-10% nominal long-term. Treasury bonds: 4-5%. Don't model anything above 10% as expected; market returns can fall short on any given decade.

How does compounding frequency affect the result? +

Monthly compounding at 7% effectively gives you about 7.23% APY. Daily compounding gives ~7.25%. Annual compounding gives exactly 7%. For most consumer scenarios, monthly compounding is the standard. The difference between daily and monthly is tiny; the difference between any compounding and simple interest is huge.

Does inflation matter? +

Yes — always. "Real" returns subtract inflation from nominal. 7% nominal in a 3% inflation environment = 4% real. For long-term planning, use real returns. For one-year purposes, use nominal returns. Inflation eats compounding silently.

What's APY vs APR? +

APY (Annual Percentage Yield): the effective annual rate after compounding — used by savings accounts. APR (Annual Percentage Rate): the simple annual rate — used by loans. A 5% APR compounded monthly has 5.12% APY. For comparing savings rates, look at APY; for loans, APR is the headline.

Should I take inflation-protected bonds? +

I Bonds: tied to inflation, $10K/year limit, tax-deferred, 0% real return floor. TIPS (Treasury Inflation Protected Securities): similar but available in any amount. Both protect purchasing power during high inflation but typically underperform stocks long-term. Good for retirement-income protection; not for growth.

Why does my high-yield savings account compound interest grow slower than my 401k? +

HYSAs are 4-5%. Stock portfolios in 401k earn 7-10% historical. The compounding math is identical — it's the rate that makes the difference. Even small rate differences compound into massive long-term differences (rule of 72: doubling time goes from 18 years at 4% to 10 years at 7%).

Should I take inflation into account on retirement projections? +

Yes. A $1M retirement target in 40 years has the purchasing power of $300K today at 3% inflation. Plan to need $2-3M for what "feels like" $1M now. The math gets dramatic over long horizons.