Compound Interest Calculator Widget

Add a compound interest calculator that handles regular saving as well as a lump sum. Readers pick annual to continuous compounding, add a monthly contribution and see the future value and a year-by-year table.

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<iframe src="https://a2z.tools/embed/w/compound-interest-calculator" title="Compound Interest Calculator by A2Z Tools" width="100%" height="830" style="border:0;width:100%" loading="lazy" allow="clipboard-write"></iframe>

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How it works

The starting amount grows with the same compound-interest engine as the A2Z Compound Interest Calculator, A = P(1 + r/n)^(nt), or P e^(rt) for continuous compounding. Monthly contributions are grown at the monthly rate that is equivalent to the chosen compounding, so a deposit and the lump sum earn at exactly the same effective rate even when interest is credited only quarterly or yearly. Contributions can be made at the start or the end of each month; start-of-month deposits earn one extra month each. The year-by-year table shows the running total paid in, the interest credited so far and the balance, which makes the point where interest starts to outpace deposits easy to spot.

Calculation method

  • Lump sum: A = P (1 + r/n)^(n t); continuous: A = P e^(r t); P = starting amount, r = annual rate / 100, n = compoundings a year (1, 2, 4, 12 or 365), t = years
  • Equivalent monthly rate: i = (1 + r/n)^(n/12) - 1 (continuous: e^(r/12) - 1)
  • Contributions (end of month): C x ((1 + i)^m - 1) / i, C = monthly contribution, m = months
  • Contributions at the start of each month are multiplied by (1 + i)
  • Interest earned = future value - starting amount - contributions; displayed to 2 decimals, table in whole units

Worked examples

Lump sum with no deposits

Inputs: 5,000 at 6% compounded annually for 20 years, no monthly contribution

Result: Future value 16,035.68; interest earned 11,035.68

The money more than triples; the interest is over twice the deposit.

Regular saving only

Inputs: 0 to start; 200 a month at the start of each month; 7% compounded monthly; 30 years

Result: Future value 245,417.50; contributions 72,000.00; interest 173,417.50

Interest supplies more than 70% of the final balance.

Continuous compounding

Inputs: 10,000 at 5% compounded continuously for 10 years

Result: Future value 16,487.21

10,000 x e^0.5; monthly compounding would give 16,470.09.

Limitations

  • Assumes a constant rate for the whole period; market investments do not grow smoothly.
  • Contributions are a fixed monthly amount; yearly increases or irregular deposits are not modelled.
  • Pre-tax and pre-fee figures.
  • Withdrawals, variable-rate accounts and tiered or bonus rates are not modelled.

Where publishers use it

  • Savings and investing blogs showing what starting early is worth
  • Bank and credit-union pages comparing daily and monthly compounding
  • Maths teachers demonstrating exponential growth with real numbers
  • Financial coaches setting monthly saving targets with clients
  • Children's savings, custodial-account and junior-ISA explainers showing decades of growth

Questions

How much difference does compounding frequency make?

Less than most people expect: 5% compounded monthly is an effective 5.12% a year, and daily is 5.13%. The rate and the number of years matter far more.

How are monthly contributions compounded when interest is annual?

Each deposit earns the monthly rate equivalent to the annual rate, (1 + r)^(1/12) - 1, so twelve months of growth equal exactly one year at the stated rate rather than slightly more.

Are taxes or fees included?

No. The result is before tax and account fees, which reduce real-world returns. A 1% yearly fee on a 7% return cuts 20-year growth by roughly a fifth.

Can I use it with no starting amount?

Yes. Set the starting amount to 0 and enter only a monthly contribution to see a pure regular-saving plan.

What is the rule of 72?

A shortcut for doubling time: divide 72 by the rate. At 7% it gives about 10.3 years; the exact figure, ln 2 / ln 1.07, is 10.24 years. 10,000 at 7% compounded monthly for 30 years reaches 81,164.97, just over three doublings.

How does this relate to the APY a bank quotes?

APY (annual percentage yield) is the effective rate after compounding. 7% compounded monthly is an APY of about 7.23%; if a bank quotes APY, enter it with annual compounding to reproduce its figures.

Does depositing at the start of the month help?

A little: 200 a month for 30 years at 7% reaches 245,417.50 with start-of-month deposits against 243,994.20 at month end, because each deposit earns one extra month.

How is continuous compounding different?

It is the mathematical limit as the compounding interval shrinks to zero, using Euler's number e. It adds only a sliver over daily compounding - at 5% for 10 years on 10,000, 16,487.21 against 16,470.09 compounded monthly.

What if my savings rate is variable?

Run the widget in stages: grow the balance for the years at the first rate, then use the result as the starting amount at the next rate. The final figure is the same as compounding the whole period at the changing rates.

Sources

  1. Compound Interest Calculator - Investor.gov, US Securities and Exchange Commission . Regulator's calculator for comparison of lump sum plus regular contributions at a chosen compounding frequency.

Cite or recommend this tool

If you reference this tool in an article, course or documentation, these formats are ready to copy. They are optional - nothing is added to your site unless you paste it.

A2Z Tools Compound Interest Calculator
https://a2z.tools/compound-interest-calculator

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