Compound Interest vs Simple Interest: The Real Difference

Simple interest is charged only on the original principal. If you deposit or borrow P at an annual rate r for t years, the interest is a constant amount each year:

interest = P × r × t, and total = P × (1 + r × t)

Simple interest is common in short-term loans, some bonds’ coupon calculations and school problems. It is also the logic behind flat-rate loans: the interest does not shrink as you repay.

Compound interest is charged on principal plus previously earned interest. With annual compounding the balance after t years is:

total = P × (1 + r)^t

With m compounding periods a year it is P × (1 + r ÷ m)^(m × t). More frequent compounding adds a little more, but with diminishing returns: going from annual to monthly makes a noticeable difference, while going from monthly to daily is small.

After 10 years the compounded balance is only about $1,300 ahead of simple interest. After 30 years the gap is about $18,200 with annual compounding. The simple-interest line has climbed by $500 a year throughout; the compound line has climbed by more each year. That is the whole story of compounding: the benefit is small early and large late.

A stated annual rate with compounding is the nominal rate (often called APR). The effective annual rate (APY) is what you actually earn over a year after compounding. For a 5% nominal rate:

• Compounded monthly, APY ≈ 5.116%.
• Compounded daily, APY ≈ 5.127%.

Banks quote APY on savings because it is the higher, more meaningful number; lenders quote APR on loans for the same reason in reverse. When you compare savings products, compare APYs. When you compare borrowing, compare effective rates including fees.

To estimate how long money takes to double at a fixed compound rate, divide 72 by the rate in percent. At 6% that gives 12 years. The exact figure is ln 2 ÷ ln 1.06 ≈ 11.9 years, so the shortcut is close. It works best for rates between about 6% and 10% and is a mental-math tool, not a replacement for a calculator.

The same rule works backwards for debts: a balance growing at 18% doubles in about four years if nothing is paid.

Credit-card balances, unpaid student loans and any debt that adds unpaid interest to the balance compound against you. The maths is identical — only the sign changes. That is why paying more than the minimum matters so much, and why the credit-card guide on this site works through a balance example.

Real savings are rarely a single lump sum. When you add contributions, the future value is the lump-sum growth plus the future value of the deposit stream. The SIP guide shows the formula and a $200-a-month example. For a quick estimate, run the lump sum in the Compound Interest Calculator and the deposits in the SIP calculator, then add the results.

Quoted rates are only comparable once they are converted to the same basis. Suppose account A pays 4.9% compounded daily and account B pays 5.0% compounded once a year. B has the higher headline rate, but A’s effective annual yield is (1 + 0.049 ÷ 365)^365 − 1 ≈ 5.02%, while B’s is exactly 5.00%. Account A therefore earns slightly more per year. The gap is small, but the same mistake with larger rate differences, or with loans, can be costly.

Always ask whether a quoted figure is nominal or effective, and how often interest is credited.

Use compound interest for savings, investments, credit cards and most loans, because interest is added to the balance. Simple interest is appropriate where the contract says so: some short-term loans, certain bond coupons that are paid out rather than reinvested, and some vehicle loans that accrue interest on the outstanding principal each day. If a statement shows interest being added to the balance, use the compound model.

• Compounding an APY again: if a bank already quotes APY, do not apply monthly compounding on top of it.
• Entering 0.05 where the form expects 5 (percent).
• Comparing a nominal rate on one product with an effective rate on another.
• Forgetting that rates, fees and taxes change over long horizons.
• Using the Rule of 72 for very high or very low rates, where it drifts.

Use the Simple Interest Calculator for loans quoted flat, and the Compound Interest Calculator for savings and investing. The APR-to-APY converter shows how much compounding frequency adds. All outputs assume the rate stays constant, which is rarely true over decades.