Project a balance with monthly deposits
Use this projection when you have a starting balance, a fixed deposit made at the end of every month, a nominal annual interest rate, and a time horizon in years. All dollar values use one currency. The annual rate is divided into 12 monthly periods; the entered years are converted to the nearest whole month.
Growth model
This is a product-defined savings scenario. With n months and monthly rate r = annual rate / 12, the initial balance grows by (1 + r)^n. End-of-month deposits use the ordinary-annuity factor ((1 + r)^n - 1) / r. At a zero rate, deposits simply equal monthly deposit times n. Total contributions are the initial balance plus all deposits; interest is final balance minus contributions.
Starting with $1,000, adding $200 monthly for 10 years at a 4.5% nominal annual rate gives $31,806.61. Contributions total $25,000 and modeled interest is $6,806.61 over 120 months. At 0%, the same deposits finish at exactly $25,000. Comparing those cases separates money deposited from the effect attributed to the rate.
Use the result carefully
Deposits are assumed constant and made after each monthly growth period. The rate never changes, and no fees, taxes, inflation, withdrawal, missed deposit, or account limit is included. The result is a projection, not a quoted account yield or guaranteed return.
Inputs must be nonnegative; years are limited to 80. Blank entries and invalid numbers are rejected. A fraction of a year is rounded to a whole number of months, so very short horizons can jump by one period. Large balances or long horizons can be highly rate-sensitive.
For a target contribution instead, use the savings goal calculator; to solve for a rate under selectable timing, use the savings interest rate calculator. This is not investment or tax advice.
Compare the deposit plan before the rate assumption
Hold the starting deposit, term, and annual rate fixed while testing another monthly contribution. Then restore the contribution and compare another rate. Save the two complete records so the projected difference can be associated with your deposit choice or the assumed growth.