One deposit, no additions, compounded
A CD takes one deposit and never receives another, so the whole calculation is compound growth on a single balance. The annual rate is divided by the compounding periods - 5% APR compounded monthly is 0.4167% a month - and applied that many times a year, with each period earning interest on the balance the last period left behind. Ten thousand dollars at 5% monthly for three years ends at $11,614.72, of which $1,614.72 is interest.
Because nothing is added, the page simply runs the savings compound calculation with contributions set to zero, which makes the result directly comparable with a savings account or a money market fund holding the same amount for the same time. The term field stops at 20 years and is rounded to whole years, the deposit is held at zero or above, and a deposit of zero returns a warning instead of a balance - there is nothing to compound.
APR versus APY on the same CD
The APR is the rate the bank quotes on the CD. The APY is what that rate really pays once compounding is counted, and on a 5% monthly quote it is 5.12%. The page prints both, because two CDs with the same APR and different compounding schedules do not pay the same, and comparing the quotes alone hides exactly that difference.
The second table makes the schedule visible: your rate priced at annual, semiannual, quarterly, monthly and daily compounding. At 5% the spread runs from 5.00% to about 5.13% - five to thirteen basis points, on a quote of five percent. That is why the APY is the number to compare between products, and why the APR is only directly comparable with another APR that compounds on the same schedule.
The trade of a locked rate
The defining feature of a CD is the commitment: the rate is fixed and the money is tied up until maturity. In return for the lock the bank pays a rate that usually beats an easy-access account, and in exchange you give up the flexibility to spend the money. That is the whole bargain - liquidity traded for certainty - and the maturity figure exists to price the certainty half of it.
Most banks charge an early-withdrawal penalty, commonly a set number of months of interest, on money taken out before the term ends, and that penalty can wipe out months of earnings. The page states the penalty in words rather than subtracting it, because the size is a contract term it does not know. Deposit insurance is the other half of the safety story: within the $250,000 per depositor, per institution, per ownership category limit, a bank failure does not cost you the deposit, but insurance never changes the rate or the penalty.
How much the compounding frequency matters
Daily, monthly and annual compounding produce different maturity balances for the same quoted APR, but over a few years the differences are small. On $10,000 at 5% for three years, the annual schedule ends around $11,576 and the daily one around $11,618 - a gap of roughly $42, or less than half a percent of the balance, for a difference in crediting that most savers would never notice.
What matters far more is the rate itself and whether you keep the money in until maturity. One extra point of APR is worth about $300 on that same $10,000 over three years, several times the entire compounding spread. So compare quotes on rate and term first, check the penalty for leaving early, and treat the compounding schedule as the last decimal rather than the deciding feature. Interest tax is not modelled here either.
The lock only pays if you stay, so price the exit
A CD quote is a rate attached to a date, and the maturity figure is only true at that date. Leave early and most banks charge a penalty measured in months of interest - commonly three months on a one-year CD, six on longer terms - which is why the honest comparison is not "5% CD versus 4% savings account" but "5% for twelve months versus 4% you can spend any day". On $10,000 at 5% compounded monthly, a full three years pays $1,614.72 of interest; leaving after six months with a three-month penalty surrenders roughly a quarter of the interest earned, and the account you move to has to beat that loss before the switch was worth it.
The other half of the lock is the rate itself: a five-year CD at 5% is a bet that five-year rates will not rise much, because the money cannot follow them up. On a 5% quote the compounding schedule is worth 5 to 13 basis points a year - real, but smaller than a single rate change - so if the term is long and the penalty is steep, ladder the deposit instead: one rung maturing each year keeps part of the money reachable without giving up the whole premium. The page prices the maturity value and the APY; the ladder is how you keep an exit.
Danfio