Compound Interest Calculator

📈How compounding actually works

Compound interest means earning interest on your interest: each period’s growth is added to the balance, so the next period earns on a larger base. The formula, with principal P, annual rate r, n compounds per year, over t years:

A = P(1 + r/n)^nt  ·  continuously: A = Pe^rt

Worked example: $10,000 at 8% compounded yearly for 10 years → 10,000 × 1.08¹⁰ = $21,589.25. That is $11,589.25 of interest — more than the original deposit. The growth accelerates: the first year earns $800, the tenth year earns about $1,599, because the balance doing the earning keeps growing.

⏱️Why compounding frequency matters

Compounding more often means interest starts earning its own interest sooner. Same $10,000 at 8% for 10 years:

Notice the diminishing returns: monthly to daily adds only $57, and daily to continuous adds under $2 — there is a mathematical ceiling (e^rt). The effective annual rate (APY) cuts through the noise: 6% nominal compounded monthly is (1 + 0.06/12)¹² − 1 = 6.16778% effective. Always compare APY, not nominal rates.

💰Adding regular contributions

Most real saving includes deposits along the way. With a monthly contribution PMT at each period’s end:

FV = P(1+r/n)^nt + PMT × [((1+r/n)^nt − 1) ÷ (r/n)]

Worked example: $10,000 starting, plus $200/month, 8% compounded monthly, 10 years. The lump sum grows to $22,196.40; the contributions grow to 200 × 182.946 = $36,589.21; total $58,785.61. You deposited $34,000 total ($10,000 + 120 × $200) and earned $24,785.61 in interest. Try it above — even $50/month from age 25 becomes serious money by 65, because contributions get decades of compounding.

That contributions field is what turns this page into a compound interest calculator with monthly contributions built in: I test a deposit habit and a lump sum in a single run, and the results card keeps my contributions separate from the interest, so I always know which dollars I put in and which dollars compounding put in.

✶️The Rule of 72

For a quick doubling estimate, divide 72 by the annual rate: at 8%, money doubles in about 9 years (check: 1.08⁹ = 1.999 — spot on). At 6%, ~12 years; at 10%, ~7.2 years. It also works in reverse: to double in 10 years you need about 7.2%. The rule is most accurate for rates between 6% and 10% — and it is a great sanity check on any projection.

⚖️Compound vs. simple interest

Simple interest pays only on the original principal: $10,000 at 8% simple for 30 years earns 10,000 × 0.08 × 30 = $24,000. Compounded yearly, the same deposit earns 10,000 × 1.08³⁰ − 10,000 = $90,626.57 — nearly four times as much. The gap is invisible early (year 5: $4,000 vs $4,693) and enormous late (year 30: $24,000 vs $90,627). That back-loaded payoff is why starting early beats investing more later: ten years of compounding at the start are worth more than ten years at the end.

🌍Think in real terms: inflation

An 8% return is not 8% richer if prices rose 3%. The real return ≈ (1 + nominal) ÷ (1 + inflation) − 1: 1.08 ÷ 1.03 − 1 = 4.854%. That $21,589.25 ten-year figure is only $16,064.43 in today’s purchasing power at 3% inflation. Inflation is the silent partner in every projection — nominal numbers impress, real numbers inform. When comparing a 5% savings account against 3% inflation versus stocks at 8% with volatility, convert everything to real terms first.

🪜One deposit, five frequencies: the 5% ladder

The table above runs at 8%, an investing-style return. When I use this page as a compound growth calculator for savings-rate money, I rerun the ladder at 5% — and the lesson flips. On $10,000 left alone for 10 years:

Monthly crediting adds about $181 over yearly. Set the frequency to Weekly — the compound interest calculator weekly mode — and I gain another $13.16. Set it to Daily and this page becomes a compound daily interest calculator; the compound interest calculator daily figure is $16,486.65, just $3.40 beyond weekly. So at savings rates the entire frequency question is worth roughly $198 on $10,000 across a whole decade: real money, but small next to a single percentage point of rate. Judged purely as a compound interest growth calculator, frequency is the least interesting lever on this page — the rate and the years are the story.

🌉From saving to investing: same formula, moving rate

Everything in this guide assumes a rate that stays put, which is exactly what a savings account offers and exactly what markets do not. When I run a decade of stock-market-style returns through this same form, I am no longer projecting a bank balance — I am using the tool as a compound investment calculator, and the smooth curve becomes an average draped over years that were really up 20%, down 10% and flat twice.

There is no shame in that: a compounding investment calculator view is the right way to set expectations over a retirement horizon, as long as I remember the line is a summary, not a schedule. My rule is simple — savings goals under five years get savings math, with a real APY from the sections below; longer goals get investment math, and for those the Investment Calculator is the tool built for the job.

🏦Your savings account, in four fields

Here is how I run this tool as a savings calculator. I put the money already sitting in my account into Principal, the account’s rate into Annual interest rate, my horizon into Time, and my automatic transfer into Monthly contribution. The math does not change — a bank account interest calculator and an investment projector are the same formula wearing different clothes — but the question changes: not “what return might I get?” but “what will this account actually pay me?” Used this way, the tool is an interest calculator savings savers can plan a deposit around: balance in, APY in, answer out.

A worked example, at an illustrative rate. Say I keep $10,000 in a high-yield account paying 4.50% APY and add $200 a month for 5 years. An APY is already the effective rate, so its monthly twin is (1.045)^1/12 − 1 ≈ 0.3675%. In the calculator above I enter 4.41% compounded monthly — the nominal rate that produces a 4.50% APY — and the Effective annual rate readout confirms 4.500%. My original $10,000 grows to $12,461.82; my 60 deposits of $200 grow to $13,398.35; the account ends at $25,860.17. I deposited $22,000 of that myself. The other $3,860.17 is interest the account paid me.

Notice the shape: my balance grows faster every year even though my deposit never changes, because the interest column compounds too. As a savings growth calculator, that interest column is the number I watch — it is the part of my balance I did not have to work for.

💹High-yield savings: what the APY really pays

APY — annual percentage yield — is the rate you actually earn in a year once compounding is counted, and under the CFPB’s deposit-account rules banks must disclose it so savers can compare accounts fairly. The nominal rate is the ingredient; the APY is the finished dish. When I use the tool above as an apy savings calculator, I always convert before I compare, because the two numbers are not interchangeable:

What is that worth in dollars? Park $25,000 for 3 years in a traditional account at an illustrative 0.50% APY and it earns $376.88 — just $125.00 in the first year. The same $25,000 at an illustrative 4.50% APY earns $3,529.15 — $1,125.00 in year one alone. Same deposit, same three years, roughly $3,152 more interest. That gap, compounding quietly, is the entire reason a high yield savings calculator is worth using before you move money: the rate difference is the product.

Two fine-print mechanics matter. Most high-yield accounts calculate interest on the daily balance and credit it monthly, so a deposit starts earning almost immediately — I model that as monthly compounding, which matches how the interest actually posts. And a high-yield APY is variable, not locked: the 4.50% I used here is an illustrative example, not a quote or a promise. When my bank moves its rate, I re-run the numbers with the new one.

🗓️Credited monthly: how savings interest is actually calculated

Because banks credit interest monthly, a saving account interest calculator monthly view is the one that matches your statement — so here is how to calculate savings account interest the way your statement does it. Step one: get the monthly rate. From an APY, that is (1 + APY)^1/12 − 1, so a 4.50% APY is 0.3675% a month. Step two: each month, multiply the balance by (1 + monthly rate) and add that month’s deposit at the end. Step three: repeat. Sixty repetitions of that loop are what carry the worked example above from $10,000 to $25,860.17 — no further formula required.

That loop is exactly what runs when I use this page as a savings calculator compound interest view — or, in the other word order people type, a compound interest savings calculator. The yearly growth table under the calculator breaks each year’s interest out separately, so I can check a bank statement line by line. If my statement’s interest for a year lands materially below the table’s figure, either my average balance was lower than I think or my rate changed mid-year — both are worth a phone call.

🧮Reading the compound formula

The compound interest equation is A = P(1 + r/n)^nt, and I read it like a sentence. A is the amount I finish with. P is the principal I start with. r is the annual rate written as a decimal — 5% becomes 0.05. n is how many times a year interest lands: 1 yearly, 4 quarterly, 12 monthly, 365 daily. t is the time in years. The exponent, nt, counts the total number of times my interest itself gets to earn interest. This is the compound interest formula in full — the same one the SEC’s Investor.gov explainer uses to teach compounding, and the only calculation this page ever performs.

The rearranged version is the interest calculation formula I reach for when I only want the earnings: Interest = A − P (minus total deposits, if I made any). And the equation for compound interest has a famous limit: let n grow — daily, hourly, every second — and (1 + r/n)^nt settles into e^rt, giving the continuous compounded interest formula, A = Pe^rt. The compounding interest formula is therefore not five formulas but one, photographed at five frequencies:

Watch me run it once, slowly, for $10,000 at 8% compounded monthly for 10 years. Per-period rate: r/n = 0.08 ÷ 12 = 0.006667. Total periods: nt = 12 × 10 = 120. Growth factor: (1.006667)¹²⁰ = 2.219640. Amount: A = 10,000 × 2.219640 = $22,196.40 — the same digits the calculator reports at the top of this page, because the tool is this formula with a friendlier face. One habit I recommend: whenever a site shows you a growth projection, spot-check one line of it by hand. If your number and the tool disagree, the tool assumed a different frequency or deposit timing — find out which before you trust the rest.