Compound interest adds earned interest to principal so the next interest calculation uses the combined balance. Simple interest uses the original principal. To compare them, specify reinvestment dates, contributions, withdrawals, taxes and costs as well as the rate. A calculation assuming a constant positive rate is different from an actual investment return.

Compare simple interest and annual compounding

All amounts in this fictional example use the same currency unit; they are not product quotations. Initial principal P =10,000, annual rate r =5%, with no contributions, withdrawals, taxes or fees. Simple interest gives P×(1+r×t); annual compounding gives P×(1+r)^t. At 10 years the balances are 15,000 and 16,288.95; at 20 years they are 20,000 and 26,532.98.

Both earn 500 in the first year. Compound interest in year two is 10,500×0.05 =525. The extra 25 comes from applying 5% to the first year's interest 500. If interest is withdrawn annually, distinguish the remaining account balance from cash held elsewhere; do not silently assume the withdrawals are reinvested.

Match the annual rate with compounding frequency

For nominal annual rate r compounded m times a year, the ending balance is P×(1+r/m)^(m×t). A nominal 5% rate compounded monthly produces a one-year effective increase of(1+0.05/12)^12−1 ≈5.1162%. Putting an already effective 5% annual rate into that monthly formula changes the stated contract assumptions.

The U.S. SEC's Investor.gov calculator separates initial amount, monthly contributions, years, estimated annual rate and compounding frequency. We checked those input meanings and verified our example independently; these are not observed results from executing the web calculator. Record whether contributions are made at the beginning or end of a month.

Debt calculations depend on the contract

The U.S. CFPB's daily-rate explanation describes some U.S. card issuers using daily balances and APR divided by 360 or 365. It is not evidence that every Korean or Japanese loan works that way, or that unpaid interest always capitalizes. Check the applicable balance, payment date, grace period, delinquency terms and capitalization rule in your own agreement. Repayment priorities also depend on required minimum payments, prepayment charges and essential cash needs.

Read the limits of a constant-growth curve

With varying returns, the balance becomes P×(1+r1)×(1+r2)… . Illustratively, +20% followed by −20% turns 10,000 into 12,000 and then 9,600, a 4% loss. An arithmetic average of 0% does not preserve principal. Apply actual fee and tax timing and a separate purchasing-power adjustment. Do not call the computed long-term balance a guaranteed return. A compounding diagram alone cannot determine a product's legality or principal guarantee; examine its contract and disclosures.