About the Interest Calculator
An interest calculator computes the interest earned on savings or owed on a loan, supporting both simple and compound interest formulas. Interest is the price of money over time — the cost charged by lenders, the return paid by savings products, and the fundamental driver of compound growth and debt accumulation. Understanding the difference between simple and compound interest, and the role of compounding frequency, is foundational to nearly every personal finance decision.
Simple interest: linear growth
Simple interest applies the rate only to the original principal: $1,000 at 5% earns $50 every year, indefinitely. After 10 years, simple interest produces $1,500. After 30 years, $2,500. The growth is linear because the interest doesn't itself earn interest — it's collected and (in lending contexts) paid out.
Simple interest is used in some short-term loans, certain car loans, U.S. Treasury bills (effectively, due to their short maturity), and some legacy financial products. Most modern consumer financial products use compound interest because compounding more accurately reflects the time value of money.
Compound interest: exponential growth
Compound interest applies the rate to the running balance — interest joins the principal and itself earns interest. Same $1,000 at 5% compounded annually: $1,050 after year 1, $1,103 after year 2, $1,629 after 10 years, $4,322 after 30 years. The 30-year balance is 73% higher than under simple interest because the later years compound on top of the earlier interest.
The longer the horizon, the larger the gap. After 50 years at 5%, simple interest produces $3,500; compound produces $11,467 — a 3.3× difference. This is why "start saving early" is the most consistent advice in personal finance, and why "start paying down debt early" is its mirror image.
Compounding frequency
The same nominal annual rate compounds to a different effective rate depending on how often interest is added. 6% compounded annually returns 6%; monthly, ~6.17%; daily, ~6.18%. Continuous compounding (the limit) returns ~6.184%. The differences are small but real over decades.
When comparing financial products, always compare APY (annual percentage yield, which includes compounding) for savings, and APR (annual percentage rate) for borrowing — they're the standardized figures that account for compounding within the year. Comparing nominal rates without considering compounding is a common cause of confusion.
Real interest: inflation-adjusted
Nominal interest is the headline rate; real interest is nominal minus inflation. A 5% savings rate during 3% inflation is a 2% real return — your purchasing power grows by 2% per year. During the 1970s, nominal savings rates often exceeded 10%, but inflation often exceeded the rates themselves, producing negative real returns.
Long-term planning should always think in real terms. A retirement projection at 7% nominal that ignores 3% inflation overstates the result substantially: $1 million in 30-year-future dollars buys roughly what $410,000 buys today. Always run two columns — nominal and real — to see what the dollars actually mean.
Formula
- I = Interest earned (simple)
- A = Final amount (compound)
- P = Principal
- r = Annual rate (decimal)
- t = Time in years
- n = Compounding periods per year
Worked examples
Simple vs. compound on $10,000 at 6% for 20 years
Simple interest: $10,000 × 0.06 × 20 = $12,000 → final $22,000. Compound (annual): $10,000 × (1.06)^20 = $32,071. Compound advantage: $10,071, more than doubling the simple-interest gain.
Effect of compounding frequency
$25,000 at 4.5% for 5 years: annual compounding = $31,160; monthly = $31,300; daily = $31,310. Differences are real but small at typical rates and modest horizons. Frequency matters more at high rates over long periods.
Real return drag
$100,000 at 5% nominal for 30 years: nominal balance $432,000. Real balance (3% inflation): $432,000 / (1.03)^30 ≈ $178,000 in today's dollars. The same growth feels very different in real-purchasing-power terms.
Frequently asked questions
What's the difference between simple and compound interest?
Simple interest applies the rate only to the original principal — interest doesn't earn interest. Compound interest applies the rate to the running balance, so interest joins the principal and itself earns. Over long horizons, compound dramatically outpaces simple interest. Most modern consumer products use compound.
How does compounding frequency affect my return?
More frequent compounding produces slightly higher returns at the same nominal rate. The effect is small at typical rates — under 0.2% over 5 years for moves from annual to daily — but real over decades and at higher rates. Always compare APY (annual percentage yield), which folds compounding into a single comparable number.
Is interest taxable?
Yes — interest from savings accounts, CDs, money markets, and most bonds is taxed as ordinary income at federal level (and usually state). Banks issue Form 1099-INT for interest of $10+ annually. U.S. Treasury interest is federally taxable but state-tax-exempt.
What is the rule of 72?
A shortcut for estimating how long money takes to double at a given rate: divide 72 by the annual rate. At 6%, money doubles in ~12 years. At 9%, ~8 years. The rule is a logarithmic approximation; it's accurate within a few percent for typical rates.
What is real vs. nominal interest?
Nominal is the headline rate. Real is nominal minus inflation. A 5% nominal rate during 3% inflation produces a 2% real return — your purchasing power grows by 2%. Long-term planning should think in real terms, since inflation continuously erodes nominal balances' purchasing power.
What's the difference between APR and APY?
APR is the annual percentage rate (typically used for borrowing) — usually expressed without considering intra-year compounding. APY is the annual percentage yield (typically used for saving) — it accounts for compounding within the year. APY is always equal to or higher than the simple rate for the same compounding frequency.