Savings and investing guide
How Monthly Savings Deposits Grow With Compound Interest
Monthly savings deposits can grow through both new contributions and interest earned on the existing balance. For a constant monthly rate and end-of-month deposits, the future value combines the compounded starting balance with an annuity of deposits. The result is an estimate under stated assumptions, not a promised account balance.
Separate the starting balance from new deposits
Let P be the opening balance, PMT the regular deposit, i the monthly interest rate, and n the number of months. With month-end deposits, future value = P(1+i)^n + PMT × [((1+i)^n − 1) ÷ i]. If i is zero, use P + PMT × n. The formula assumes equal deposits and a constant rate.
Worked example with USD
Suppose you start with $1,000, add $200 at the end of each month for 24 months, and assume 0.3% interest per month. The starting balance grows to about $1,074.54; the deposits grow to about $4,969.30. The combined estimate is about $6,043.84 before taxes or fees. The $4,800 of deposits plus the initial $1,000 account for $5,800 of principal; the rest is modeled interest.
Deposit timing changes the result
The formula above assumes each $200 deposit arrives at month-end. If deposits arrive at the beginning of each month, each deposit earns one additional month of interest, so the projected balance is higher. Actual payroll transfers can land on different dates, and banks may calculate interest using daily balances. Use account terms and a conservative estimate when the date matters.
Convert an annual rate carefully
A simplified monthly model often divides a nominal annual rate by 12. A disclosed APY already reflects compounding over a year, so dividing APY by 12 is not exactly the same calculation. A bank may calculate daily interest and credit it on a schedule. Read the account disclosures and match the calculator’s rate convention to the rate you enter.
What the projection leaves out
A constant-rate estimate does not account for variable rates, withdrawals, deposits that change, taxes, fees, or inflation unless those are modeled. On a taxable account, interest may be reportable income. For a short-term goal, avoid relying on uncertain investment returns to meet a fixed date. If your account pays no interest for one month, the actual balance will also be lower than a model that assumes the same rate every period; compare the projection with account statements as you save.
Use a target-based check
If the goal is a specific amount by a specific month, compare the projected balance with the goal and adjust the contribution or timeline. For instance, if a projection ends at $6,044 and the target is $6,500, the roughly $456 gap should be addressed with a higher deposit, a later date, or a lower target—not by assuming an unearned rate.
Frequently asked questions
Does deposit timing matter?
Yes. A beginning-of-month deposit has one more modeled period to earn interest than a month-end deposit.
Can I divide APY by 12?
That is only an approximation for some purposes. APY already reflects annual compounding; match the calculator convention to the account disclosure.
Sources and further reading
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