Compound Interest Daily Calculator

Daily compound interest is interest calculated on your balance every day and added to it, so tomorrow's interest is computed on a slightly larger amount. With 365 periods a year the formula is A = P(1 + r/365)^(365t). The interest-on-interest effect is real but small at savings rates: on $10,000 at 5% it earns $1.05 a year more than monthly compounding.

For a single deposit: A = P x (1 + r/365)^(365 x t), where P is the deposit, r the annual nominal rate as a decimal and t the years. For regular deposits, each one compounds from its own date; for deposits at every compounding period the annuity term is PMT x [((1 + r/365)^(365t) - 1) / (r/365)]. The APY is (1 + r/365)^365 - 1.

Not for typical savings balances and horizons. At 5% APR on $10,000, daily compounding earns $1.05 more than monthly over one year and $6.44 more over five. The APYs are 5.127% and 5.116%. A competing account paying 0.10 points more earns about ten times as much extra, so compare accounts on APY rather than compounding schedule.

APR is the nominal annual rate the bank divides by 365 to get the daily rate. APY is what you earn over a full year including compounding: APY = (1 + APR/365)^365 - 1, so 4.5% APR is a 4.602% APY and 5% APR a 5.127% APY. To go the other way, APR = 365 x ((1 + APY)^(1/365) - 1). The APY is the figure to compare across accounts.

Yes. The APY is the effective yield after the account's compounding schedule, so 4.60% APY means $10,000 earns $460 in a year with no other activity. The nominal rate behind it on a daily-compounding account is about 4.498%; enter 4.498 in the Annual return field to reproduce the account. Entering 4.60 would overstate a year's interest by about $10.71.

Compare the APYs; the higher one wins whatever the schedule. 5.20% APR monthly is a 5.326% APY; 5.25% APR daily is a 5.390% APY, so the daily account is ahead. If the monthly account paid 5.30% APR instead, its APY would be 5.431% and it would win. Never compare APR with APR across different compounding schedules.

It depends on the rate. At a 4.5% rate compounded daily (4.602% APY), $10,000 earns $460.25 in a year with no further deposits; at 5% it earns $512.67. At a quoted 4.5% APY it earns exactly $450. Savings rates are variable, so check the current APY before projecting beyond a few months.

Yes. Set the Regular contribution and its frequency; each deposit compounds daily from the date it is made. A $5,000 balance plus $200 a month at 4.5% APR for three years reaches $13,416.79 — $12,200 paid in and $1,216.79 of interest. The annual ledger shows the balance at the end of each year.

Both. Compounding daily means interest is calculated every day on a balance that includes the interest accrued so far; paying (crediting) monthly means the accumulated interest appears in the account once a month. The growth rate is set by the daily compounding, so a "4.50% APY, compounded daily, credited monthly" account earns what the daily formula predicts.

365 days a year, the convention most US savings and money-market accounts use for daily compounding. Some instruments use a 360-day year, which gives a slightly higher effective yield for the same nominal rate; if yours does, enter the APR x 365/360 as the annual return. Your account disclosure states the method the bank uses.

No — results are pre-tax. Savings interest is generally taxable as ordinary income in the year it is credited. At a 22% marginal rate a 4.5% yield is about 3.51% after tax; enter that as the annual return for an after-tax projection. Check IRS Topic 403 for how interest income is reported.

Divide the annual target by the APY. $12,000 a year needs $300,000 at a 4.00% APY, about $342,857 at 3.50%, or $240,000 at 5.00%. Those are pre-tax figures: at a 22% federal rate the $1,000 is about $780 after tax, before any state tax. Because savings rates move with Federal Reserve policy, the balance needed can change substantially from year to year.