How it works
Contributions are assumed to be made at the end of each month. With monthly compounding, each month: balance = balance × (1 + r/12) + contribution, which matches the future-value formula
FV = P(1 + i)n + C × ((1 + i)n − 1) / i
where i = annual rate ÷ 12 and n = months. With annual compounding, interest is credited once a year: the starting balance earns the full annual rate and each monthly deposit earns simple interest for the months remaining in that year. The required monthly contribution for a goal is solved from the same formula.
Worked examples
$500/month at 7% for 30 years, monthly compounding
Final balance: $609,985.50. You contribute $180,000.00 and earn $429,985.50 in interest.
$5,000 start + $300/month at 4% for 10 years, annual compounding
Final balance: $51,415.61 ($41,000.00 contributed, $10,415.61 interest). To reach $50,000 instead (monthly compounding), you'd need about $288.94 per month.