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Savings Growth with Monthly Deposits or a Lump Sum

Model a starting balance with beginning-of-month deposits, or a separate one-time investment, using an entered constant return.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Use the result with context

Results are estimates for planning and education. Confirm rates, taxes, fees, and legal requirements with the relevant institution or a qualified professional before making a financial decision.

Formula and method

With 1,000 initially and twelve beginning-of-month deposits of 100, a zero return gives a final balance of 2,200 and total interest of zero.

Monthly deposits: FV = P(1+i)^N + D[(1+i)^N − 1](1+i)/i; at i = 0, FV = P + ND

Worked example

Enter these known values and leave the other values blank.

Starting balance
1000 USD
Deposit at the beginning of each month
100 USD / mos
Entered annual rate — see mode convention
0 %
Investment period
12 yrs / mos
Total deposit
2200 USD
Total interest
0 USD
Projected value with monthly deposits
2200 USD

Assumptions and limitations

  • Monthly-deposit mode divides a nominal annual rate by twelve and applies deposits at the beginning of each month. One-time mode instead compounds the entered annual rate annually. These rate conventions are different.
  • The entered rate is constant and nonnegative. The calculation excludes taxes, fees, rate changes, withdrawals and account-specific terms.
  • Time is positive. A fractional number of payment periods uses a mathematical extension of the annuity formula, not a dated deposit schedule.
  • Zero interest is calculated directly as the starting balance plus total deposits. A flat balance with no deposits does not determine a unique investment duration.

Common questions

Is the annual rate an APY?

Monthly-deposit mode expects a nominal annual rate divided by twelve, not an effective APY. One-time mode treats the entered rate as an annual compound rate.

When are monthly deposits made?

At the beginning of each month, so each deposit earns one more month of interest than an end-of-month deposit.

References

Bookify accepts zero return and requires nonnegative accumulation amounts and a positive duration. Bookify evaluates the zero-interest limit directly, including available reverse calculations; nonzero-rate source expressions are preserved.

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