Where does my monthly saving land?

What a fixed amount added every month or every year does to a balance, and how much of the result is growth rather than what you paid in. It does not account for tax or fees, and the balance it reports is nominal, so what it buys is the real return calculator's question.

After 10 years the balance is 94,111. The regular contributions account for 77,641 of it, and the starting balance and its own growth for the rest, assuming the rate holds for the whole period.

Each contribution earns a return for the time it is in the account and no longer. Money added in the first year compounds for the whole term; money added in the last year barely compounds at all. The balance is what you started with, grown over the full term, plus every contribution grown over its own remaining term.

The rate is annual and the frequency divides it, so choosing monthly applies a twelfth of the rate twelve times a year. That is what a rate quoted per year and compounded monthly means. Choosing monthly also multiplies what you pay in by twelve, and of the two effects that is by far the larger one, which is why the second figure names the number of payments behind it.

P(1 + i)^n + C × ((1 + i)^n − 1) ÷ i

P is what you start with, C is one contribution, i is the rate for a single period, and n is the number of periods.

A worked example

Start with 10,000 and add 500 a month at 5% a year for ten years. You pay in 70,000 counting what you started with, the balance reaches 94,111, and 24,111 of it is growth.

What it assumes

• Each contribution lands at the end of its period, which is what a standing order into a savings account does. Paying at the start of each period instead would give every contribution one more period of growth.
• The rate is fixed for the whole term. Real products reprice, and a rate advertised for an introductory period is not the rate for the term.
• Nothing is withdrawn along the way. A balance drawn on partway through does not reach these figures, and the earlier the withdrawal the wider the gap.
• The figures are nominal. Where a currency is losing value, what the balance will buy is a separate question from what it will say, and the real return calculator is where that one is answered.