How CD Interest Is Calculated: Compounding and APY Explained

A bank advertises a five-year CD at “4.50% APY”, you deposit $10,000, and five years later the statement shows $12,523. Where did the extra $23 beyond 4.5% a year come from, and why does a different bank at the same rate pay $12,508? This guide explains how CD interest is calculated, from the compound formula to the APY on the sign, using the CD calculator to check each number. It also covers the early withdrawal penalty and the tax bill, which are the two things the sign leaves out.

What a CD is

A certificate of deposit is a bank deposit with a fixed term, from one month to ten years, and a fixed interest rate for that term. You agree not to touch the money until maturity; in return the bank pays a higher rate than a savings account. Deposits are FDIC-insured (or NCUA-insured at a credit union) up to $250,000 per depositor per bank. At maturity you take the money, roll it into a new CD, or let it renew automatically, usually at whatever rate the bank is offering that day.

The compound formula

Maturity value = P × (1 + r ÷ k)^(k × t)

• P is the deposit.
• r is the annual interest rate as a decimal, so 4.5% is 0.045. This is the rate, not the APY; the difference is explained below.
• k is how many times a year interest is added to the balance: 365 for daily, 12 for monthly, 4 for quarterly, 1 for annual.
• t is the term in years.

Each time interest is added, the next period’s interest is calculated on the larger balance. That is compounding, and the more often it happens, the slightly more you earn.

,000 at 4.5% for five years

Daily and monthly compounding differ by $5 over five years. The gap between any compounding and simple interest is bigger, $270, because simple interest never earns on itself. The CD calculator lets you pick the compounding; use monthly if you are not sure, since the result is within a few dollars of daily.

Rate versus APY

Banks quote two numbers. The interest rate is r in the formula. The annual percentage yield is what one year of compounding at that rate actually produces: APY = (1 + r ÷ k)^k − 1. At a 4.5% rate compounded daily, the APY is 4.602%; compounded monthly, 4.594%.

By law the APY must appear on the advertisement, which is why two banks with different compounding but the same APY pay the same. When comparing CDs, compare APY to APY and ignore the compounding. When using the formula or the calculator, enter the rate; the calculator shows the effective yield, which is the APY, next to the result.

A one-year CD at 4.5% compounded daily on $10,000 pays $460 of interest, and the APY line will say 4.60%. The difference between 4.5% and 4.6% is $10 on $10,000; it is not nothing, but it is not the number to shop on.

When interest is credited and paid

Most CDs add the interest to the balance at each compounding period and pay it all at maturity. Some, especially longer terms and larger balances, offer to pay the interest out monthly or quarterly to a checking account instead. A paid-out CD earns simple interest, because the interest never stays in the account to compound, which is the last line of the table. If you need the income, take it; if you do not, let it compound.

The first statement after opening may show less interest than you expect because the first period was partial. The term runs from the funding date, not the application date.

The early withdrawal penalty

Breaking a CD before maturity costs a penalty set by the bank, usually expressed as a number of months of interest: 3 months on a one-year CD, 6 to 12 months on a five-year CD are common. On the $10,000, 4.5% five-year CD, a six-month penalty is $225. The penalty comes out of the interest earned, and if you withdraw early enough it can eat into the principal.

Two consequences. First, a CD you might need to break is worth comparing against a high-yield savings account with no penalty; the CD must pay enough more to cover the penalty risk. Second, if rates rise sharply after you buy a long CD, breaking it and buying a new one at the higher rate can pay: compare the penalty against the extra interest over the remaining term. Federal rules set a minimum penalty of seven days’ interest for withdrawals in the first six days; everything else is the bank’s choice, so read the disclosure.

Taxes

CD interest is taxed as ordinary income in the year it is credited to the account, whether or not you withdraw it. On a five-year CD you receive a Form 1099-INT every year for that year’s interest, not one at maturity, and you pay tax on money you cannot touch. In the 22% bracket, the $2,523 of interest on the example costs about $555 in federal tax over the five years, plus state tax where it applies. CDs inside an IRA defer the tax; CDs in a taxable account do not.

Breaking a CD when rates rise, worked

Suppose you bought the five-year CD at 4.5% and two years later new five-year CDs pay 5.5%. Breaking costs six months of interest, $225, and the balance after two years is $10,942 before the penalty, $10,717 after. Reinvested at 5.5% for the remaining three years, that grows to $12,639. Left alone, the original CD reaches $12,523. Breaking wins by $116, barely; at a new rate of 5.0% it loses. The rule: break only when the rate gain over the remaining term clearly exceeds the penalty, and run the numbers in the calculator rather than guessing.

CD ladders

A ladder splits the money across terms, say $2,000 each in one-, two-, three-, four- and five-year CDs. Each year one matures; you spend it or roll it into a new five-year CD at the current rate. After four years every rung is a five-year CD and one matures every year. The ladder gives most of the five-year rate with yearly access and reduces the risk of locking everything in at a bad time. The savings plan calculator is the tool for the monthly-deposit version of the same idea.

Checking your own CD

Open the CD calculator, enter the deposit, the rate (not the APY) and the term, and pick the compounding from the bank’s disclosure. The maturity value should match the figure on your confirmation to within a dollar or two. If the bank only gave you the APY, enter it with annual compounding; the result is the same. For a lump sum that may need to stay liquid, compare with the retirement savings calculator or a savings account before you lock it in. All the tools are on the homepage.

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