What This Calculator Does
This Compound Interest Calculator with Monthly Contributions shows how an initial lump sum plus regular monthly deposits grow over time when interest compounds monthly. It is ideal for planning savings goals, retirement contributions, or any account where you invest a starting amount and keep adding to it each month.
How to Use It
Enter your initial investment (the money you start with), your monthly contribution (the amount you add every month), the annual interest rate as a percentage, and the number of years you plan to invest. The calculator returns your projected future balance, the total amount you deposited, your total contributions, and the interest you earned.
The Formula Explained
The result combines two parts. The first, \(P\left(1+\frac{r}{12}\right)^{12t}\), grows your starting principal with monthly compounding. The second, \(PMT\times\frac{\left(1+\frac{r}{12}\right)^{12t}-1}{\frac{r}{12}}\), is the future value of an ordinary annuity — it sums every monthly contribution and the interest each one earns. Here \(r\) is the annual rate as a decimal, \(t\) is years, and contributions are assumed to be made at the end of each month.
$$A = P\left(1+\frac{r}{12}\right)^{12t} + PMT\cdot\frac{\left(1+\frac{r}{12}\right)^{12t}-1}{\frac{r}{12}}$$
Worked Example
Suppose you start with $10,000, add $200 each month, earn 6% annually, and invest for 10 years. The monthly rate is \(0.06/12 = 0.005\) over 120 months. The principal grows to about $18,193.97, and the contributions grow to about $32,775.87, giving a future balance of roughly $50,969.84. You deposited $34,000 total, so you earned about $16,969.84 in interest.
$$I = A - \left(P + PMT\times 12t\right)$$
FAQ
Is compounding monthly or annual? This tool uses monthly compounding, matching the monthly contribution schedule.
Are contributions made at the start or end of the month? They are treated as end-of-month (ordinary annuity) deposits.
What if the interest rate is 0%? The calculator handles a 0% rate correctly — your balance is simply the principal plus all contributions with no interest.
