What This Calculator Does
This tool projects how much an investment or savings account will grow when you start with an initial lump sum and add a fixed amount every month, with interest compounding monthly. It combines two engines of growth: your original principal earning compound interest, and a stream of monthly deposits that each earn interest from the moment they land.
How to Use It
Enter your initial principal (the amount you start with), your monthly deposit, the annual interest rate as a percentage, and the term in years. The calculator returns your projected future balance, the total amount you actually contributed, the interest you earned, and a breakdown showing how much growth came from the principal versus the deposits.
The Formula Explained
The future value is the sum of two parts. The first, \(P\left(1 + r/12\right)^{12t}\), grows your starting principal at the monthly rate \(r/12\) over \(12t\) months. The second, \(\text{PMT}\cdot\left[\dfrac{\left(1 + r/12\right)^{12t} - 1}{r/12}\right]\), is the future value of an ordinary annuity — it sums up each monthly deposit plus the interest it accrues. If the rate is zero, the deposit portion simply becomes \(\text{PMT}\times\text{number of months}\).
$$A = P\,(1+r)^{n} + D\cdot\frac{(1+r)^{n}-1}{r}$$where
$$\left\{ \begin{aligned} P &= \text{Initial Principal} \\ D &= \text{Monthly Deposit} \\ r &= \dfrac{\text{Annual Rate (\%)}}{100\times 12} \\ n &= 12\times\text{Term (years)} \end{aligned} \right.$$
Worked Example
Start with $1,000, add $100 per month at 6% annual interest for 10 years. The monthly rate is \(0.005\) and there are \(120\) months. The principal grows to about $1,819.40, and the deposits grow to about $16,387.93, for a total of roughly $18,207.33. You contributed $13,000, so you earned about $5,207.33 in interest.
$$A = 1000\,(1.005)^{120} + 100\cdot\frac{(1.005)^{120}-1}{0.005} \approx 1{,}819.40 + 16{,}387.93 = 18{,}207.33$$FAQ
Are deposits added at the start or end of the month? This uses an ordinary annuity, where deposits are made at the end of each period.
Does it account for taxes or inflation? No. Results are nominal, pre-tax figures. Reduce the rate to estimate real (inflation-adjusted) growth.
What if I only want a lump-sum projection? Set the monthly deposit to 0 and the tool acts as a pure compound interest calculator.
