Compound Interest with Monthly Contributions
Plain compound interest covers a single lump sum. Real wealth is built by combining compounding with regular monthly contributions — a SIP, an auto-transfer to savings, a 401(k) match. This is the formula behind that machine, with worked examples showing why even small monthly amounts become enormous.
The formula
If you deposit M at the start of every month for m months at a monthly rate i, the future value of the contributions alone is:
FV = M × [ ((1 + i)^m − 1) / i ] × (1 + i)If you also start with a balance P, add its own compounding on top:
Total = P × (1 + i)^m + M × [ ((1 + i)^m − 1) / i ] × (1 + i)
The monthly rate is the annual rate divided by 12 (10% p.a. → 0.00833). The trailing (1 + i) assumes
each deposit lands at the start of the month — the standard convention for SIPs. Compare this with the single-sum
formula A = P(1 + r/n)^(nt) to see how the contributions term was added.
A 30-year worked example
Invest $500 per month at 9% p.a. for 30 years:
| Year | Total Contributed | Balance | Growth in that balance |
|---|---|---|---|
| 5 | $30,000 | $37,700 | $7,700 |
| 10 | $60,000 | $93,000 | $33,000 |
| 20 | $120,000 | $320,000 | $200,000 |
| 30 | $180,000 | $915,000 | $735,000 |
Look at the last two rows: from year 20 to year 30 you contributed only $60,000, yet the balance grew by ~$595,000. By year 30, 80% of the balance is growth, not money you put in. The interest is earning interest on interest — the compounding snowball. Numbers like these are exactly what the SIP Calculator produces.
Why small monthly amounts snowball
Each deposit becomes a tiny lump sum growing for a different number of years. The first deposit grows for the whole tenure; the last deposit barely at all. Because the oldest deposits do most of the work, the curve bends upward sharply near the end — which is why a 30-year plan can dwarf a 15-year plan even at the same monthly amount. Two years of extra contributions at the end can add more than ten years of contributions at the start.
What a yearly step-up changes
If your contribution rises 10% per year (tracking salary growth), the final balance balloons while the blended annual return may dip, because recent, larger deposits have had less time to compound. Both numbers are real: the corpus is what you retire on, and XIRR is how efficient the plan was. The SIP Calculator includes a step-up field so you can see the trade-off live.
Keep it in real terms
Inflation cuts every one of those nominal balances. At 6% inflation, a nominal $915,000 in 30 years is worth roughly $160,000 in today's money — still a healthy multiple of the $180,000 contributed, but far from the headline figure. Read how inflation affects investments, then run the plan with an inflation assumption in the Timeline Simulator.