Compound interest with monthly contributions: formula and example
Separate deposits from growth and understand how contribution timing, compounding and inflation change a savings projection.
What grows and what you contribute
A larger ending balance can come from deposits, investment growth or both. Always compare the projected balance with the total cash you put in. A constant-rate calculation is a scenario: real investment returns can vary and capital can fall.
Use matching periods
For a nominal annual rate r compounded monthly, the monthly rate i is r ÷ 12. Convert a percentage to a decimal first: 6% becomes 0.06. Over t years there are n = 12 × t periods. If the input is an effective annual rate instead, i = (1 + r)^(1/12) − 1. These conventions are different.
Formula for month-end deposits
With initial balance P and a fixed month-end contribution C, future value = P × (1 + i)^n + C × ((1 + i)^n − 1) ÷ i. At zero interest use P + C × n; do not divide by zero. For deposits at the beginning of each month, multiply only the contribution term by (1 + i).
Worked example
Start with 1,000, add 100 at each month-end and assume a nominal annual rate of 6%, compounded monthly, for one year. The projected balance is 2,295.23. Total deposits are 2,200, so modeled growth is 95.23. Beginning-of-month deposits would produce 2,301.39. Try the compound interest calculator, checking its contribution and compounding settings. Keep precision during calculation and round money only at the end.
Make the scenario useful
Test a lower rate, a shorter saving period and a missed contribution rather than relying on one optimistic balance. Fees, taxes and inflation can reduce spendable value. For purchasing-power comparisons, divide future money by an assumed inflation factor; do not simply label the nominal balance as today’s money. Plan an affordable contribution using the monthly budget guide and work backward from a target with savings goals.
Common questions
Can CAGR measure my investment return when I make deposits? Endpoint CAGR can be misleading because it treats added money as growth. Read CAGR versus average growth before choosing a method.
Does monthly compounding guarantee this outcome? No. The formula guarantees only the arithmetic for the stated assumptions, not a market return or an account provider’s terms.
Reference
Investor.gov compound interest calculator provides a public tool for exploring initial balances, contributions, rates and compounding frequency.