Monthly Compound Interest Formula With Monthly Contributions
The monthly compound interest formula with monthly contributions is FV = P(1 + r/12)12t + PMT × [((1 + r/12)12t − 1) / (r/12)]. The first term grows your starting balance; the second grows your recurring monthly deposits. For example, $10,000 up front plus $500 a month at 7 percent for 20 years grows to about $300,851 — $40,387 from the initial sum and $260,463 from the contributions, on $130,000 paid in. This page breaks the formula into its two parts with verified examples.
The two parts of the formula
Compound interest with monthly contributions is really two calculations added together. Most people already have some money saved and plan to keep adding to it, so the formula tracks both at once:
- The starting balance — a single lump sum that compounds on its own.
- The monthly contributions — a stream of equal deposits, each of which compounds from the moment it lands until the end.
Because the deposits keep arriving, the second part usually grows into the larger of the two over a long horizon, even when the starting balance is not small.
The formula, term by term
Written in full, the future value is:
Each symbol has a plain meaning:
- P — the starting balance (present value).
- PMT — the amount added at the end of each month.
- r — the annual interest rate as a decimal (7 percent is 0.07).
- r/12 — the monthly rate, since interest compounds once a month.
- t — the number of years; 12t is the number of months.
The first term is ordinary future value of a single sum. The second is the future value of a monthly contribution stream — an ordinary annuity. Add them and you have the whole picture.
Worked example: $10,000 + $500 a month
Take a $10,000 starting balance, $500 added every month, 7 percent a year compounded monthly, over 20 years (240 months). Here is how the two parts combine:
| Component | Formula piece | Value after 20 years |
|---|---|---|
| Initial $10,000 | P(1 + r/12)12t | $40,387 |
| $500 / month | PMT × [((1 + r/12)12t − 1)/(r/12)] | $260,463 |
| Combined | sum of the two | $300,851 |
You pay in $130,000 over those 20 years — the $10,000 start plus $120,000 of deposits — so roughly $170,851 of the final total is compound growth. Notice how the contributions ($260,463) dwarf the grown lump sum ($40,387): steady monthly investing does most of the heavy lifting.
Run your own numbers: the compound interest calculator applies this exact formula — enter a starting balance, a monthly contribution, a rate and a timeline to see both pieces combined.
How the balance builds over time
The same $10,000 + $500 a month at 7 percent, checked at four points. Watch the interest column pull ahead of what you have paid in:
| Years | Total balance | Paid in | Compound growth |
|---|---|---|---|
| 5 years | $49,973 | $40,000 | $9,973 |
| 10 years | $106,639 | $70,000 | $36,639 |
| 15 years | $186,971 | $100,000 | $86,971 |
| 20 years | $300,851 | $130,000 | $170,851 |
At five years growth is a modest slice; by twenty it is larger than everything you contributed. That crossover is compounding doing its work, and it is why starting early matters more than almost anything else.
Why monthly compounding
Dividing the annual rate by 12 and counting periods in months mirrors how most real accounts and investment contributions actually behave — money goes in monthly and interest is credited on the running balance. Compounding annually instead would use (1 + r)t and give a slightly lower figure, because the balance would sit uncompounded for longer between credits.
Every calculator and figure on this site uses monthly compounding for exactly this reason, so the numbers here line up with what the tools return. For the difference between the frequencies, see how compound interest works.
Calculating it without the math
You do not need to work the formula by hand. Match your goal to the right tool:
- Balance plus monthly deposits — the compound interest calculator takes a starting amount and a monthly contribution together.
- Long-term portfolio growth — the investment growth calculator models regular contributions and compounding returns.
- A specific savings target — the savings growth calculator focuses on reaching a goal with steady deposits.
All three apply the same monthly math shown here, so their results match the formula.
Assumptions
- Monthly compounding. The annual rate is divided by 12 and applied each month, matching this site's calculators.
- End-of-month deposits. Contributions are treated as ordinary-annuity payments made at the end of each month.
- Constant rate and contribution. The rate and the monthly amount are held steady for the full term; real returns and deposits vary.
- Nominal figures. Results are before inflation, tax and fees, all of which reduce real growth.
Frequently asked questions
The bottom line
The monthly compound interest formula with contributions simply adds two familiar pieces: a lump sum that compounds and a stream of monthly deposits that compounds. Split it that way and it stops looking intimidating — $10,000 plus $500 a month at 7 percent reaches about $300,851 in 20 years, and the deposits do most of the work.
To skip the algebra entirely, drop your own numbers into the compound interest calculator, and read future value with monthly contributions for a deeper look at the deposit half of the formula.
Disclaimer: This guide is for general educational purposes only and is not financial advice. The examples use assumed rates of return to illustrate the formula; they are projections, not guarantees, and actual results vary with markets, inflation, taxes and fees. Consider speaking with a qualified financial professional before making decisions about your own money.