Future value grows the starting balance by the monthly rate and grows each contribution for the months it stays invested. With a zero rate, the result is only the sum of the deposits.
Future value = start × (1 + i)ⁿ + contribution × ((1 + i)ⁿ − 1) ÷ i
Here i is the monthly rate. An annual rate is converted to the monthly rate that compounds to the same year. Contributions land at the end of each month, which is the ordinary annuity.
A short example: 1,000 at 1% a month for 12 months, plus 100 at the end of each month, reaches 2,395.08.
How to read the result
Total deposited is the starting amount plus every contribution, before interest. Interest earned is the gap up to the future value. The calculation does not remove taxes, fees or inflation.
Questions
When does the contribution enter the balance?
At the end of each month. The starting amount earns for the whole month. That month's contribution starts earning the following month.
Is the annual rate the monthly rate times twelve?
No. Twelve percent a year becomes the monthly rate (1 + 0.12) ^ (1 ÷ 12) − 1, about 0.9489% a month.
What does the one-thousand example return?
One thousand to start, 1% a month, twelve months and a contribution of one hundred reach 2,395.08. Of that, 2,200 was deposited.
Does the result remove tax?
No. Income tax, fees and inflation stay out of the future value.