Compound interest calculator with contributions

The balance grows month by month. Each month the balance you already have earns interest, and only then the new contribution is added: balance = balance x (1 + rate) + contribution.

That is why the contribution of a given month does not earn interest in that same month. It is the end-of-period convention, the one any real investment uses when you deposit at the end of the month.

This calculator repeats that line once per month instead of applying a closed formula, which is what lets it show you the balance at every step and separate how much is your own money from how much is interest.

Because dividing by 12 gives the proportional rate, which only makes sense for simple interest. With compound interest the correct conversion is the equivalent rate: monthly rate = (1 + yearly rate) ^ (1/12) - 1.

The difference is easy to check. 10% per year divided by 12 gives 0.8333% per month, but 0.8333% compounded for 12 months comes back as 10.47% per year, not 10%. The conversion contradicts itself.

This is the most common mistake in the subject, and it is why this calculator prints the monthly rate it actually used.

In simple interest only the initial amount earns interest, so the balance grows in a straight line. In compound interest the interest itself starts earning interest, and the balance grows as a curve.

For one month both give the same number. The gap opens with time, and it opens fast: it is the reason the interest column in the table above eventually passes the contributions column.

Run the calculation and read the table: the crossing point is the first period where the interest column is bigger than the contributions column.

It depends on three things and not only on the rate. A large initial amount brings the crossing closer, a large monthly contribution pushes it away, because it keeps adding money that has not had time to earn anything yet.