Compound Interest Calculator
See how principal grows with compound interest. Choose compounding frequency and optional contributions each period to model savings or investments.
Written and maintained by Ricardo Rodrigues · Last updated · What changed
Who this calculator is for
This page projects a balance when interest stays in the account and the rate you type is applied, unchanged, for the whole term. It is a scenario tool: a savings illustration, a textbook problem, a comparison of “start now” against “start five years later.” It is not a market forecast, not a loan schedule, and not a promise from a bank. Fees, tax, and inflation are absent unless you have already reduced the rate to stand in for them — and if you do that, say so.
People use it to see that contributions often dwarf the opening deposit, and that compounding frequency matters less than they were told at ordinary savings rates. The chart of numbers is the constant-rate path. Real accounts wander.
Compound Interest Calculator
Project growth with compound interest and optional regular contributions
Compounding frequency
Contribution is applied once per compounding period (e.g. monthly when compounding monthly).
Result
$31,998.32
Interest earned $9,998.32 · Contributed $22,000.00
FV = P(1+r/n)^(nt) + PMT × [((1+r/n)^(nt)−1) ÷ (r/n)]
Final balance
$31,998.32
Total contributed
$22,000.00
Interest earned
$9,998.32
120 compounding periods
Comparison table
| Compounding | Value after 10 years | Effective annual rate |
|---|---|---|
| Yearly | 1,628.89 | 5% |
| Quarterly | 1,643.62 | 5.095% |
| Monthly | 1,647.01 | 5.116% |
| Daily | 1,648.66 | 5.127% |
Frequency matters less than the rate and the time. Going from yearly to daily adds about 0.13 percentage points of effective rate at 5%.
About this compound interest
The projection multiplies a balance by (1 + rate/periods) once per period, and it can add a contribution series on top. Ten thousand euros at 5% for ten years, compounded monthly and left alone, grows to about €16,470. The same nominal rate compounded only once a year lands a bit lower. Daily compounding lands a bit higher. The rate you type moves the result more than the frequency toggle does, at ordinary savings rates.
Contributions often dominate the ending balance. One hundred euros a month alongside that €10,000 example is a second pile, and most of those euros do not get a full ten years of growth. The chart is a scenario at a constant rate, not a market forecast and not a loan schedule.
How to use each field
- Starting principal
- The amount already there at the beginning, before any contribution and before any interest. €10,000 goes here in the usual example. It earns interest for the full term. Later contributions do not.
- Annual interest rate
- The nominal annual rate, the one advertisements quote before you ask about frequency. 5 means 5% a year, split across the number of compounding periods. It is not automatically the effective annual rate. At monthly compounding, 5% nominal is about 5.116% effective.
- Years
- The length of the scenario. 10 years at monthly compounding is 120 periods. A fractional year is allowed by the formula; a bank may not offer the same flexibility. Zero years returns the principal and no interest.
- Contribution per period
- An extra deposit once per compounding period, treated as an end-of-period contribution. If you compound monthly, this box is a monthly contribution. If you compound annually, it is a yearly one. The helper text under the frequency control says this, and it is the easiest field to misread. Zero means the lump sum is left alone.
- Compounding frequency
- Annually, semi-annual, quarterly, monthly, or daily (365). The nominal rate is divided by that count. Daily at 5% is a slightly higher ending balance than monthly, which is slightly higher than annual. At ordinary rates the gap is real and smaller than a change in the rate itself.
When to use this calculator
- You want to see a lump sum at a stated rate and frequency, with the interest left in the account.
- You want to compare “I start now” with “I start five years later” by changing the term.
- A bank advertises daily compounding and you want the euro gap versus monthly at the same nominal rate.
Worked examples
| Question | Answer |
|---|---|
| $10,000 at 5% for 10 years (monthly) | About $16,470 without contributions |
| $10,000 + $100 per period at 5% | Higher balance from contributions + interest |
| $5,000 at 7% for 20 years annually | About $19,348 |
Walkthroughs
€10,000 left alone, then the same account with €100 a month
Principal 10000, rate 5, years 10, contribution 0, frequency monthly. Ending balance about €16,470. Interest is about €6,470, because you only put in the original 10,000. Switch the contribution to 100. You have now added €12,000 over 120 months. The ending balance is the grown lump sum plus the future value of that series. Most of the new money was not invested for the full decade, so you do not get €12,000 × 1.647. The page’s “total contributed” line includes the original principal and every deposit. Subtract it from the final balance and what remains is interest. That split is the part worth reading. The headline balance mixes your own money with the bank’s.
Starting five years late
Same 5% monthly, contribution 100, but years = 5 instead of 10, principal 10000. You will see a lower balance, and the gap versus the ten-year run is not just “five years of €100.” The early deposits in the ten-year version had extra years to compound, and the original principal had extra years too. The late start is the expensive one. This is still a constant-rate cartoon. It is a good cartoon for the cost of waiting, and a bad one for predicting a fund that can fall.
Formula
| Goal | Formula |
|---|---|
| Future value (no PMT) | P(1 + r/n)^(nt) |
| With contributions | P(1+r/n)^(nt) + PMT × [((1+r/n)^(nt) − 1) ÷ (r/n)] |
With no contributions, future value = P × (1 + r/n)^(n×t). P is principal, r is the annual rate as a decimal, n is periods per year, t is years. €10,000 at 5% for 10 years compounded monthly: n = 12, exponent = 120, growth factor ≈ 1.647, balance ≈ €16,470. The same nominal rate compounded once a year is 10,000 × (1.05)^10 ≈ €16,289. The frequency gap is about €180. A 6% annual rate on the same lump sum is 10,000 × (1.06)^10 ≈ €17,908. The one-point rate change beats the frequency toggle.
Contributions use the ordinary annuity factor: payment × (((1 + r/n)^(nt) − 1) ÷ (r/n)), added to the grown principal. That factor assumes a deposit at the end of each period, which matches this page. €100 a month beside the €10,000 example is 120 deposits, €12,000 of new money, and those deposits do not all get ten years of growth. The last one barely earns anything. The interest figure the page reports is ending balance minus principal minus every contribution. It is not “the rate times the total.”
A loan is a different shape. An amortizing payment is sized so the balance hits zero, and interest is charged on a falling balance. Negative contributions in this tool are not a substitute unless the amount happens to be the exact payment. Use the loan calculator for installments. Simple interest, which does not pay interest on interest, is the comparison in the simple-versus-compound guide: 5% simple on €10,000 for 10 years is €5,000 of interest and a €15,000 ending balance, short of the compound figure.
Mistakes this page will not catch for you
Using it as a loan payment calculator
An amortizing loan charges interest on a falling balance and sets a payment so the balance hits zero. That is not a compound-growth curve with a negative deposit unless the deposit happens to be the exact payment. Use the loan calculator for installments.
Reading a nominal rate as a promise
The tool compounds whatever percent you type, every period, without fees, tax, or inflation. A 7% illustration is a scenario. Label it as one before you treat the cents as a balance you will have.
Reading a nominal rate as an effective one, or the reverse
If a bank quotes 5.12% AER and you type 5.12 into a monthly compounder, you have compounded an already-effective rate and overstated the balance. The effective-annual-rate guide shows the conversion. Type the nominal rate the contract compounds, or reduce an AER to nominal before you choose a frequency.
FAQ
- What is compound interest?
- Interest is calculated on principal plus previously earned interest. Over time this creates exponential growth compared with simple interest.
- How often should interest compound?
- More frequent compounding (e.g. monthly vs annually) slightly increases effective yield for the same nominal annual rate.
- Why isn’t monthly compounding dramatically better than annual?
- At 5% over ten years on €10,000 the gap is on the order of a couple of hundred euros, not a second fortune. The effective annual rate moves from 5% to about 5.12%. Over decades the gap grows, and it is still smaller than a real difference in the nominal rate.
- Does the contribution earn interest immediately?
- Each contribution compounds for the periods that remain after it is added, not for the whole term. The last payment barely earns anything. That is why the future value of the series is less than “total contributed times the full growth factor.”
- Why isn’t monthly dramatically better than annual?
- At 5% for ten years on €10,000 the gap is on the order of a couple of hundred euros. The effective annual rate moves from 5% to about 5.12%. Over long periods the euro gap grows. It still loses to a real difference in the rate you were able to get.
- Does the tool withhold tax on the interest?
- No. Many countries tax interest or investment gains. The balance here is a pre-tax scenario at a constant rate. A careful comparison uses an after-tax rate you computed yourself, and labels it as after-tax.
- What does daily compounding assume about the year?
- 365 periods, not 360 and not 366. Banks differ. At ordinary savings rates the convention changes the result by a small amount. If you are matching a contract to the cent, read the contract’s day count. This page is the 365 version.
Guides that go with this calculator
- Compound Interest BasicsHow compounding frequency and regular contributions change a balance, with a simple-interest contrast and the assumptions a calculator quietly makes.
- Simple vs Compound InterestSimple interest stays on the original principal. Compound interest pays interest on interest. A side-by-side balance sheet shows when the gap is small and when it takes over.
- Effective Annual RateTurn a nominal rate and a compounding frequency into the true one-year growth factor, and see why daily compounding is a small edit to the rate rather than a new product.
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