Compound Interest Monthly Calculator

A = P(1 + r/12)^(12t) + PMT x [((1 + r/12)^(12t) - 1) / (r/12)], where P is the starting balance, r the annual rate as a decimal, t the years and PMT the end-of-month deposit. For a lump sum with no deposits it is A = P(1 + r/12)^(12t). The effective annual yield (APY) is (1 + r/12)^12 - 1.

Monthly compounding credits interest 12 times a year instead of once. At 6% APR, annual compounding gives exactly 6.000% and monthly an APY of 6.168%. On $10,000, monthly compounding earns $16.78 more than annual in one year and about $1,031 more over 20 years with no deposits. Real, but modest.

APY (annual percentage yield) is the effective annual return after compounding. For monthly compounding, APY = (1 + r/12)^12 - 1: 5% APR is a 5.116% APY and 6% APR a 6.168% APY. US banks must disclose the APY on deposit accounts under Regulation DD; it is the figure that compares directly across compounding schedules.

At 5% APR with no further deposits: $10,511.62 after 1 year, $12,833.59 after 5, $16,470.09 after 10, $27,126.40 after 20 and $44,677.44 after 30. Every ten years multiplies the balance by the same 1.647 — that is the compounding curve. Enter your own balance, rate and horizon for any other combination.

Choose "Solve for a savings goal", then enter your starting balance, rate, time horizon and target. The end-of-month formula is PMT = (Target - P x GF) x (r/12) / (GF - 1), with GF = (1 + r/12)^(12t). To reach $100,000 in 10 years from $5,000 at 6% APR: GF = 1.819397, P x GF = $9,096.98, and PMT = $90,903.02 x 0.005 / 0.819397 = $554.69 a month.

Then the deposit needed is $0.00: the starting amount alone, compounded at the rate you entered for the time you entered, reaches the target. The headline shows $0.00 and the detail line says what the starting amount grows to. That is the correct answer, not an error — you may not need to save anything more for that goal.

At 5% APR from $0: $200 a month takes 23 years, $400 a month 15 years, $600 a month 11 years and $800 a month 9 years. Starting from $10,000: $400 a month takes 13 years and $600 a month 10. Use the goal tab and adjust the years until the deposit matches what you can actually save — amount and time are the two levers that matter.

Each deposit earns interest from the month it is made, so regular deposits compound on their own. $5,000 alone at 6% APR grows to $16,551 in 20 years; adding $300 a month takes it to $155,163. The deposits are $72,000 of that, and their growth most of the rest. The composition bar below the result shows the three-way split.

It depends almost entirely on time and the return assumed. At 7% compounded monthly, reaching $1,000,000 from zero takes about $381 a month over 40 years, $820 over 30 years or $1,920 over 20 years. Doubling the horizon from 20 to 40 years cuts the deposit by about 80%. These are nominal, pre-tax figures; $1 million in 30 years buys much less than today.

Subtract what you have from the target and solve for the deposit at a savings rate. For $60,000 from zero, with no interest you need $60,000 / 60 = $1,000 a month. At 4% compounded monthly the deposit drops to about $905 a month, because interest covers about $5,700 of the goal. For money needed on a fixed date within a few years, a savings or CD rate is the realistic assumption.

If you already have the money, depositing it at once earns more, because every dollar compounds from day one. $12,000 deposited today at 5% compounded monthly is worth $12,613.94 after a year; the same $12,000 as $1,000 at the end of each month reaches $12,278.86 — about $335 less. The rule is to deposit what you have as early as you can.

Enter the nominal rate (APR); the calculator shows the APY beside the result. If you only have the APY, convert it: APR = 12 x ((1 + APY)^(1/12) - 1), so a 5.116% APY is a 5.00% APR. Entering the 5.116% APY directly would overstate a year's interest on $10,000 by about $12, and the gap grows over long horizons.