Finance & Loan
Compound Interest Calculator
See what your savings grow into once interest starts earning interest — including regular monthly contributions.
Compound Interest Calculator
About the Compound Interest Calculator
Compound interest is interest earning interest. Leave the returns in place and they start generating returns of their own, so growth accelerates rather than proceeding in a straight line. Over long periods the difference against simple interest is enormous.
This calculator handles a starting balance, regular contributions, and any compounding frequency from daily to annually. It shows what you put in and what the interest added, separated out — which is the comparison that actually makes the case for starting early.
You can also choose whether contributions land at the start or the end of each period. It is a small setting that makes a real difference over decades, and the page explains why.
How to use the Compound Interest Calculator
- Enter your starting amount — use 0 if you are beginning from nothing.
- Enter the yearly interest rate and how many years you will save for.
- Choose the compound frequency. More frequent compounding gives a slightly higher result at the same rate.
- Add a regular contribution if you pay in each month, and set how often you pay it.
- Select Calculate future value, then read the year-by-year table to see when interest starts outpacing your contributions.
The formulas
Lump sum : A = P(1 + r/n)nt
Contributions: A += PMT × [ ((1 + r/n)nt − 1) ÷ (r/n) ]
Simple interest: A = P(1 + rt) — for comparison
P = starting amount, r = annual rate as a decimal, n = compounds per year, t = years, PMT = contribution per period.
Worked example
£10,000 invested for 20 years at 6%, compounded monthly, with no further contributions.
A = 10,000 × (1 + 0.06÷12)240 = 10,000 × 1.005240
£33,102 — of which £23,102 is interest
Simple interest at the same rate would give £22,000. Compounding added £11,102 for doing nothing except leaving the returns alone.
Simple interest formula vs compound interest
The simple interest formula is I = P × r × t, so interest is calculated only on the original amount. Compound interest is calculated on the original amount plus everything earned so far. On £10,000 at 6%:
| Years | Simple interest | Compounded monthly | Difference |
|---|---|---|---|
| 5 | £13,000 | £13,489 | £489 |
| 10 | £16,000 | £18,194 | £2,194 |
| 20 | £22,000 | £33,102 | £11,102 |
| 30 | £28,000 | £60,226 | £32,226 |
| 40 | £34,000 | £109,575 | £75,575 |
The gap does not grow steadily — it accelerates. That is the whole argument for starting early: the last decade of a 40-year run adds more than the first three combined.
How much does compounding frequency matter?
Less than people expect. Going from annual to monthly compounding helps; going from monthly to daily barely registers. On £10,000 at 6% for 20 years:
| Compounded | Final amount | Effective annual rate |
|---|---|---|
| Annually | £32,071 | 6.000% |
| Quarterly | £32,907 | 6.136% |
| Monthly | £33,102 | 6.168% |
| Daily | £33,198 | 6.183% |
| Continuously | £33,201 | 6.184% |
The whole span from annual to continuous is worth about £1,130 over twenty years — real, but far less than a 0.25% difference in the rate itself. Chase the rate, not the compounding frequency.
Effective annual rate = (1 + r/n)n − 1
Continuous compounding : A = Pert
The effective annual rate is what lets you compare accounts quoting different compounding frequencies. In the UK it is called the AER.
Contributions at the start or the end of the period
Contributing at the start gives each payment one extra period of growth. It is a small edge that compounds:
- £200 a month for 20 years at 6%, paid at the end: about £92,408.
- The same, paid at the start: about £92,870 — roughly £462 more.
The mechanism is simply time. If you can set a standing order for the 1st rather than the 28th, you may as well take it. It is a marginal gain, not a strategy.
What this calculator does not include
The result is a nominal, pre-tax figure at a constant rate. It does not deduct tax on interest or gains, does not account for platform or fund fees, and does not adjust for inflation. It also assumes a steady return, which savings accounts roughly deliver and investments emphatically do not — real market returns are volatile, and sequence matters.
To see what your final figure is worth in today's money, run it through the inflation calculator. At 6% nominal with 2.5% inflation, that £33,102 after 20 years buys about what £20,200 buys today.
The rule of 72
A quick mental check: divide 72 by the interest rate and you get roughly the years to double your money.
- At 3% — about 24 years.
- At 6% — about 12 years.
- At 9% — about 8 years.
It is an approximation, accurate to within a few percent for rates between about 4% and 12%, and useful for sanity-checking any growth claim in your head.
This is a calculation aid, not financial advice. It does not know your circumstances, and nothing here is a quote, an offer or a recommendation. Rates, fees, tax rules and lending regulations change constantly and differ by country and provider. Before committing to anything, get figures in writing from the provider and, where the amounts matter to you, take advice from a qualified adviser who knows your situation.
Compound, simple and continuous interest formulas
Here are the main interest formulas in one place. In each one, P is the starting amount, r the yearly rate as a decimal, t the number of years and n the number of times interest compounds per year.
Simple interest: I = P × r × t
Compound interest: A = P × (1 + r/n)n×t
Continuous: A = P × er×t
Effective annual rate: EAR = (1 + r/n)n − 1
The continuous interest formula, A = Pert, is the upper limit — interest added every instant. It sounds dramatic, but it adds very little over daily compounding. At 5% for 10 years, $10,000 grows to $16,487.21 with continuous compounding and $16,486.65 with daily compounding — a gap of 56 cents.
Effective annual interest rate formula (APY)
Banks often quote two numbers. The nominal rate is the headline rate. The effective annual rate — often called APY — includes the effect of compounding. Compare savings accounts using APY.
The effective annual rate formula and the APY formula are the same thing: APY = (1 + r/n)n − 1. A 4.5% rate compounded monthly gives (1 + 0.045/12)12 − 1 = 4.594% APY. To turn a monthly interest rate into an annual one, use the same idea: 0.5% a month is (1.005)12 − 1 = 6.17% a year, not 6%.
| Nominal rate 5% | Compounds per year | Effective annual rate |
|---|---|---|
| Yearly | 1 | 5.000% |
| Monthly | 12 | 5.116% |
| Daily | 365 | 5.127% |
| Continuous | ∞ | 5.127% |
CD compound interest calculator: monthly or daily
Use it as a certificate of deposit compound interest calculator. A certificate of deposit (CD) is a fixed sum, a fixed rate and a fixed term. That makes it easy to model here. Enter the deposit, the CD rate and the term in years. Set Compound frequency to match the bank — usually monthly or daily. Leave the regular contribution at zero, since most CDs do not accept top-ups.
Worked example
$25,000 in a 1-year CD at 4.5%.
Compounded monthly, it earns $1,148. Compounded daily, it earns $1,151.
Difference: about $3 a year
If the CD pays interest out each month instead of compounding, the monthly interest is simply 25,000 × 0.045 ÷ 12 = $93.75.
The rate and the term matter far more than the compounding frequency. Shop for the rate first.
Compound interest table
What $10,000 grows to with yearly compounding and no extra deposits:
| Rate | 5 years | 10 years | 20 years | 30 years |
|---|---|---|---|---|
| 3% | $11,593 | $13,439 | $18,061 | $24,273 |
| 5% | $12,763 | $16,289 | $26,533 | $43,219 |
| 7% | $14,026 | $19,672 | $38,697 | $76,123 |
| 10% | $16,105 | $25,937 | $67,275 | $174,494 |
Add monthly saving and the numbers jump. $500 a month at 7%, compounded monthly for 30 years, grows to about $610,000 — from $180,000 of deposits. That is why compound interest matters so much for a Roth IRA, 401(k) or any long-term account.
Reverse compound interest calculator: find the rate
Know where you started and where you ended up? You can work out the yearly rate that got you there.
r = (ending amount ÷ starting amount)1/t − 1
Example: $10,000 became $20,000 in 8 years. (20,000 ÷ 10,000)1/8 − 1 = 0.0905. The money grew at about 9.05% a year. To see how rising prices eat into that, try the inflation calculator.
Compounded semi-annually or quarterly
Bonds often pay twice a year, and many savings accounts credit interest every quarter. Divide the rate by the number of periods and raise to the number of periods in total. For $10,000 at 6% over 10 years:
- Compounded annually: 10,000 × 1.0610 = $17,908.
- Compounded semi-annually: 10,000 × (1 + 0.06/2)20 = $18,061.
- Compounded quarterly: 10,000 × (1 + 0.06/4)40 = $18,140.
Pick Half-yearly or Quarterly in the compound frequency box to get the same answer above.
Compound interest calculator with withdrawals
Taking money out each month? The same formula works in reverse: growth adds to the balance, and each withdrawal takes away.
Balance = P(1 + i)n − W × [ ((1 + i)n − 1) ÷ i ]
i = rate per period, n = number of periods, W = withdrawal per period.
Two quick examples show how it behaves:
- $100,000 at 6%, taking $500 a month. The monthly interest is exactly $500, so the balance never moves. You can draw that amount forever.
- $100,000 at 5%, taking $800 a month. Withdrawals now beat growth. The money runs out after about 14 years 9 months.
This calculator only adds contributions, so use the formula above for withdrawals. If your withdrawals are smaller than the interest earned, the balance keeps growing.
Increasing contributions
Most people save more as their pay rises. That makes a big difference over time. $300 a month at 7% for 30 years grows to about $366,000. Raise that $300 by 5% every year and the total jumps to about $633,000.
To model increasing contributions here, run the calculator in stages: one run for the first few years, then feed the result in as the starting amount for the next run with a bigger contribution.
Compound interest savings account options
Not every compound interest account works the same way. Here is where compound interest shows up most:
- High-yield savings and money market accounts — usually compound daily and pay monthly. Rates change with the market.
- Certificates of deposit — a fixed rate for a fixed term, compounded daily or monthly.
- Roth IRA and 401(k) — the account itself does not pay interest, but reinvested growth compounds in the same way. A Roth IRA adds a bonus: qualified withdrawals are tax-free, so the compound interest is never taxed.
- Bonds and Treasury notes — pay interest twice a year. Reinvest it and it compounds semi-annually.
Compare savings accounts on APY, check whether the rate is variable, and look for monthly fees that can wipe out the interest on a small balance.
Other ways to use this calculator
The same compounding maths fits most savings products.
- CD calculator compounded daily or monthly — set the compound frequency to match your bank and leave contributions at zero.
- Compound savings calculator — for a savings account, enter the balance, the APY as the rate and your monthly deposit.
- Effective annual rate calculator — use the APY formula above to turn any nominal rate into the effective annual rate.
- Cumulative interest calculator — the Interest earned line is the total interest added over the whole period.
- Compound interest calculator with monthly contributions — enter a regular contribution and how often you add it.
- Reverse compounding calculator — use the reverse formula above to find the rate from a start and end value.
- TSP, 401(k) and S&P 500 compound interest calculator — enter your balance, contribution and an expected return. The S&P 500 has averaged roughly 10% a year before inflation over the long run, but single years swing hard, so test a lower rate too.
- Compound interest calculator with inflation — use your expected return minus inflation as the rate. 7% growth with 3% inflation is roughly 4% in today’s money.
- Savings growth calculator and investment calculator — enter a starting balance, monthly deposits and an expected return.
- Future value calculator — the final balance is the future value of your money.
- Interest compounding — switch the frequency to see what monthly or daily compounding adds.
Frequently asked questions
Compound interest is interest calculated on your original amount plus everything already earned, so returns start generating returns. £10,000 at 6% compounded monthly becomes £33,102 after 20 years, against £22,000 with simple interest — a difference of £11,102. The effect accelerates over time, which is why the last decade of a long run contributes more than the first three.
Less than most people assume. On £10,000 at 6% over 20 years, annual compounding gives £32,071 and daily gives £33,198 — about £1,130 across the whole range. Going from monthly to daily is worth under £100. A 0.25% better interest rate beats any change in compounding frequency, so compare the effective annual rate (AER) rather than the schedule.
The start, if you have the choice. Each contribution then gets one extra period of growth. Over 20 years at 6%, £200 a month contributed at the start of each month produces roughly £462 more than the same amount contributed at the end. It is a small, free gain — worth taking if your standing order date is flexible, but not worth reorganising your finances for.
No. The figures are nominal and pre-tax: no tax on interest or gains, no platform or fund fees, and no inflation adjustment. It also assumes a constant rate, which savings accounts approximate and investments do not. To see the result in today's money, run it through the inflation calculator — at 2.5% inflation, £33,102 in 20 years buys about £20,200 worth today.
A = P(1 + r/n)^(nt). P is the starting amount, r is the yearly rate as a decimal, n is how many times interest compounds each year and t is the number of years. Subtract P from A to get the interest earned.
A = Pe^(rt), where e is about 2.71828. It gives the most interest possible at a given rate, but only slightly more than daily compounding. $10,000 at 5% for 10 years becomes about $16,487.
Yes. Enter the deposit, the CD rate and the term, then set the compound frequency the bank uses, usually monthly or daily. Leave the regular contribution at zero. The result shows the interest the CD will earn by maturity.
Grow the balance at the rate per period and subtract each withdrawal. In formula form: Balance = P(1 + i)^n minus W times ((1 + i)^n minus 1) divided by i. On $100,000 at 5%, withdrawing $800 a month uses up the money in about 14 years 9 months.
A = P(1 + r/4)^(4t). For $10,000 at 6% over 10 years that is 10,000 times 1.015 to the power 40, which equals $18,140. Semi-annual compounding uses r/2 and 2t instead and gives $18,061.
APR is the yearly rate without compounding. APY includes compounding, using APY = (1 + r/n)^n minus 1. A 4.5% APR compounded monthly is a 4.594% APY. Use APY to compare savings accounts.
Not as interest from the account itself, but the investments inside it grow and that growth compounds when you reinvest it. Because qualified Roth IRA withdrawals are tax-free, all of that compound growth stays yours. Use this calculator with an expected return to estimate it.
Sources and further reading
- Consumer Financial Protection Bureau — Compound interest — how compounding works on savings and debt
- MoneyHelper — Savings and AER explained — the effective annual rate and comparing accounts
- US SEC Investor.gov — Compound interest calculator — a regulator-published equivalent
- Federal Reserve — Savings interest rate data — published benchmark interest rates