Compound interest with monthly savings: how the growth works
Compound interest is interest paid on interest. Each period, the balance earns a rate, and that interest joins the balance so it earns in the next period too. The formula is A = P(1 + r/n)^(nt), where P is the starting amount, r the annual rate as a decimal, n the number of compounding periods a year, t the years and A the final amount. The compound interest calculator adds monthly contributions on top, which the basic formula does not cover, and shows a year-by-year table.
Compound interest calculatorWhat will my savings grow to?OpenThe formula, step by step
Take 10,000 at 5% a year, compounded monthly, for 10 years. The rate per month is 0.05 ÷ 12, and the number of months is 10 × 12 = 120. So A = 10,000 × (1 + 0.05/12)^120. The monthly factor is about 1.00417, and raised to the 120th power it is about 1.64701. Multiply by 10,000 and the result is 16,470.09. The calculator gives the same figure for these inputs.
A second check: 1,000 at 10% a year, compounded yearly, for 2 years is 1,000 × 1.10 × 1.10 = 1,210.00. The interest in year two is earned on the interest from year one, which is why the total is more than the 1,200 that simple interest would give.
What compounding frequency changes
Compounding frequency is how often interest is added to the balance: yearly, quarterly, monthly or daily. More frequent compounding gives a slightly higher return for the same nominal rate, because interest starts earning sooner. The gap is small. A 5% nominal rate gives an effective annual rate of 5.00% compounded yearly, 5.12% compounded monthly and 5.13% compounded daily. Frequency adds about a tenth of a percentage point. The rate and the time do far more. Going from 5% to 6% is a much bigger change than going from monthly to daily, and ten years does more than five.
So when you compare two savings accounts, look at the rate first, and at the effective annual rate if the provider gives one. Frequency is a detail to check, not the main decision.
Adding monthly contributions
Regular saving changes the picture. The calculator adds each contribution at the end of each month. Using the standard annuity formula, 100 a month at 5% compounded monthly for 10 years, starting from nothing, gives about 15,528. That is 12,000 paid in and about 3,528 of interest. This figure is worked out by hand with the formula, as an illustration, and is not output from the tool.
Two points follow. Most of the final amount is money you paid in. And the interest on early payments has more time to grow than the interest on late ones. A payment made in the first year earns for almost ten years here, while one made in the last month earns almost nothing. That is why starting early usually matters more than saving a larger amount late.
The rule of 72
For a quick estimate, divide 72 by the annual rate in percent. The answer is roughly how many years it takes for money to double. At 6%, 72 ÷ 6 = 12 years. The exact figure for 6% is about 11.9 years, so the rule is close. At 10%, the rule gives 7.2 years against an exact 7.27. The rule is most accurate at moderate rates, and it drifts further from the true value at very high ones.
Inflation: the real return
A balance that grows at 5% a year does not give 5% more buying power if prices also rise. To estimate the real return, divide (1 + nominal rate) by (1 + inflation rate) and subtract 1. If an account pays 5% and prices rise by 3%, the real gain is about 1.94%, because 1.05 ÷ 1.03 − 1 is 0.0194. The calculator shows nominal figures, so adjust them yourself if you want a real-terms view.
What the calculator does not do
The calculator assumes one fixed rate for the whole period. It does not model taxes, fees, or returns that move up and down, as shares do. Those can change the result a lot, and a fixed-rate projection can make a volatile investment look steadier than it is. Treat the output as arithmetic about a stated rate, not as a forecast.
This is general information, not investment advice. If you are deciding where to put money, check the terms with a regulated adviser or the provider's official documents.
When you borrow, interest works against you instead. The loan calculator shows monthly payments and the total interest on a loan. The percentage calculator helps when rates are quoted in different ways and you need to compare them.
Quick answers
What is the formula? A = P(1 + r/n)^(nt). Divide the annual rate by the number of periods a year, raise the result to the total number of periods, and multiply by the starting amount.
Does monthly compounding beat yearly by a lot? Not much. At 5%, the difference is about 0.12 percentage points a year.
When does a monthly contribution start earning? The calculator adds it at the end of each month, so it earns interest only for the months after it is paid.
