How CD Interest Is Calculated: APY, Compounding, and Penalties
CD interest follows A = P(1 + r/n)^(nt). Why banks quote APY and not the rate, how compounding frequency moves the total, and what breaking early costs.
A certificate of deposit grows by the compound interest formula
A = P(1 + r/n)^(nt), wherePis your deposit,ris the nominal annual rate,nis how many times a year the bank credits interest, andtis the term in years. Because banks advertise APY, which already folds compounding in, the shortcut isA = P(1 + APY)^t.
Want the balance without the algebra? Our CD calculator takes the deposit, the APY, the term, and the compounding schedule, and returns the value at maturity, the interest earned, and what an early exit would cost. The rest of this page explains what it is doing and where hand math goes wrong.
The formula, and the one input people get wrong
A CD is the compound interest formula wearing a bank's clothes. Your deposit is the principal, the term is the time, and the bank's schedule sets how often interest is calculated and added back. Three of the four inputs are printed on the paperwork and hard to get wrong.
The rate the formula wants is the nominal rate, not the advertised one. An annual percentage yield already contains the compounding, so feeding an APY into a formula that compounds it again counts the same effect twice. Convert first, in whichever direction you need, and the two numbers stay consistent.
APY and the interest rate are not the same number
Banks in the United States must disclose an annual percentage yield on deposit accounts, and the Truth in Savings rules define exactly how it is computed (Regulation DD, Appendix A). That is why APY, not the headline rate, compares two banks fairly. APY is always at least as high as the nominal rate, and equal only when interest compounds once a year or is paid out instead of reinvested.
Start with an advertised yield on an account that credits interest monthly. Convert the yield down to the nominal rate the formula wants, then run it. The one-year answer lands exactly on the advertised yield, which is the entire point of APY.
Now make the mistake on purpose. Type the advertised yield into the formula as though it were the nominal rate and compound it monthly. The balance comes out too high, and the gap widens every year, because you have quietly promised yourself a better account than the one you opened.
One naming note, because the search box asks for it constantly. A deposit account has no APR. That term comes from the lending rules and describes the cost of borrowing. A CD has a stated interest rate and a legally defined APY, so anyone quoting a CD "APR" means the nominal rate.
What compounding frequency actually changes
Hold the deposit, the nominal rate, and the term fixed, and change only how often interest is credited. Each step up in frequency raises the balance, because interest starts earning interest sooner, and each step raises it by less than the one before. The sequence runs into a ceiling at the continuous-compounding limit.
Read that as yields and the effect shrinks further. The spread from annual to daily on the same rate is a few hundredths of a percentage point. Federal rules set no required compounding frequency for deposit accounts, which is exactly why the yield rather than the rate is the comparable number (Regulation DD, interest calculation). Compare two CDs on APY and the frequency question has already answered itself.
What breaking a CD early costs
Banks price the early-withdrawal penalty as a number of months of interest on the amount withdrawn, charged at the CD's own rate. Two details do the damage. The penalty is simple interest on the principal, not a share of what you actually earned, and it is not capped at the interest sitting in the account. Break the CD before you have accrued enough to cover it and the shortfall comes out of your deposit.
Penalty tiers rise with the term. Those below are the common shape of a schedule, not a rule and not a quote. Your own disclosure is the only authority on your CD.
Now break one early. Cash the same account out after three months against a six-month penalty. The penalty is roughly double the interest earned, so less money lands in your account than you put in, and the annualized return is negative.
Hold the same CD longer and the arithmetic flips. The penalty is fixed the moment you sign, while accrued interest keeps climbing, so there is a crossover point after which an early exit still leaves you ahead of your deposit. On this account it arrives at around six months, and by the middle of the second year the exit is comfortably profitable, just at a worse yield than holding to maturity.
Federal rules do set a floor, but a narrow one. Withdraw within the first six days after depositing and the penalty must be at least seven days' simple interest. Beyond that window the penalty is whatever your account agreement says, and there is no federal ceiling on it (OCC, HelpWithMyBank). The penalty schedule is required to be in your disclosures, so read it before the rate.
Why savers build CD ladders
A ladder splits one pot across several CDs that mature a year apart, then rolls each maturing rung into a fresh long-term CD. After the first cycle every rung is earning close to the long rate, yet one rung is always within twelve months of coming due. That is the trade it solves: you want the yield that comes with a long lock-up, and you also want not to be locked out of your own money for years.
The blended yield lands between the shortest rung's rate and the longest one's, which is the honest summary of a ladder. You give up yield against putting everything into the longest term, and you buy back a penalty-free exit every year. The ladder builder on the CD calculator lets you set each rung to the rate your own bank is quoting.
Where your arithmetic and the bank's number legitimately differ
Even done correctly, a hand calculation can miss the bank's figure by a few cents or a basis point. Four reasons, all mundane, all real.
The last one is the big one and it is almost never mentioned. If the CD pays interest into a checking account each month instead of adding it back, nothing compounds, the account earns plain simple interest, and its yield is allowed to equal its stated rate. Two CDs advertising the same headline rate can pay differently for that reason alone, so check whether interest is credited to the CD or paid away from it before comparing anything.
What to check before you sign
Compare CDs on APY and nothing else, then read the penalty schedule before you read the rate again. The rate sheet decides what you earn if you hold to maturity, and the penalty schedule decides what you keep if you cannot.
Common questions
Roughly the yield times the deposit. A one-year CD earns almost exactly its APY, because APY is defined as the one-year return. Over longer terms the interest compounds, so a five-year hold earns more than five times the one-year figure.
Both are common, and neither is required, because the rules leave the frequency to the institution. Daily compounding edges out monthly on the same nominal rate, but the difference is small enough that it is never the reason to pick one CD over another.
Strictly, a CD has no APR. Deposit accounts disclose an interest rate and an annual percentage yield, while APR belongs to the lending rules and describes borrowing costs. When a bank or an article says "CD APR" it means the nominal rate, and the yield you actually earn on it is higher whenever interest compounds more than once a year.
You get the balance accrued to that date minus the penalty, which is usually a set number of months of interest on the amount withdrawn. Because that penalty is priced on your principal rather than on what you have actually earned, an early exit in the first months of a term can hand back less than you deposited.
Three routes, in descending order of usefulness. A no-penalty CD can be closed after a short initial waiting period at no cost, in exchange for a lower rate. A ladder puts a rung within twelve months of maturity at all times. And a brokered CD can be sold on the secondary market rather than surrendered, though the price you get moves with rates and can be below what you paid.
In the United States, yes. Interest on a CD held in a taxable account is ordinary income at your marginal rate, taxed in the year it is credited and available to you rather than the year the CD matures, so a multi-year CD can generate a tax bill on money you cannot yet touch (IRS, interest received). An early-withdrawal penalty is separately deductible. Interest inside an IRA CD is tax-deferred or tax-free instead. This is general information, not tax advice.
CDs at a member bank are covered by federal deposit insurance, and share certificates at a member credit union are covered by the NCUA Share Insurance Fund. The cover applies per depositor, per institution, per ownership category, and it includes accrued interest up to the limit (FDIC, NCUA).
It is a liquidity strategy, not a yield strategy. A ladder earns less than putting everything into the longest term and more than rolling everything at the shortest, and in exchange one slice of your money comes free every year. If you know you will not need the cash, a single long CD pays more. If you might, the ladder is what buys the option.
