Compound Interest with Regular Deposits: Worked Examples

Separate money you add from interest earned

A growing balance has two sources: your contributions and interest on money already in the account. Reporting the whole increase as “interest” overstates the gain when you make regular deposits. A useful projection shows the ending balance, total contributions and their difference.

The Compound Interest Calculator accepts a starting principal, annual nominal rate, duration, compounding frequency and monthly contribution. It assumes contributions arrive at month-end. The examples use currency-neutral amounts: use dollars, rupees or another currency consistently, with no exchange conversion. The current tool labels its monetary results “Rs.”; the numerical growth calculation itself does not change with currency.

Monthly compounding with month-end deposits

Let P be the starting principal, D the fixed monthly deposit, i the monthly decimal interest rate and N the number of whole months. For a nominal annual decimal rate j compounded monthly, i = j/12.

Future value = P(1+i)^N + D × ((1+i)^N − 1)/i

The first term grows the original balance. The second adds deposits with different time in the account: D[(1+i)^N−1 + … + (1+i) + 1]. The final deposit earns no interest before the end point because it arrives at that point. At i = 0, use P + DN instead of dividing by zero.

Start with 1,000 and add 100 monthly at 6%

Select monthly compounding, principal 1000, contribution 100, annual rate 6 and duration 1 year. The monthly rate is 0.06/12 = 0.005. After 12 months, the future value is 2,295.23. You supplied 1,000 + 12 × 100 = 2,200.00, so interest is 95.23.

After two years, contributions total 3,400.00 and interest is 270.36. Without any monthly deposits, the original 1,000 alone would grow to 1,061.68 after one year. This separates the effect of saving more from the effect of compounding.

Beginning-of-month deposits change the answer

If all 12 deposits arrive at the beginning of their months instead, each gets one extra month of growth. Multiply only the deposit term by (1+i), leaving the original principal term unchanged. The one-year example becomes 2,301.40, about 6.17 more than month-end deposits.

That beginning-of-month result is a manual comparison, not a selectable timing feature in this calculator. A missed deposit or a mid-month payment needs a different cash-flow schedule. Keep full precision until displaying the final amount; actual institutions may round interest as it is credited.

Other compounding frequencies and fractional years

For m compounding periods per year and t years, the tool grows principal using P(1+j/m)^mt. It converts that growth into an equivalent monthly rate for contributions: i = (1+j/m)^m/12 − 1. Monthly deposits are then valued with that i. This is a mathematical interpolation; an account that credits interest annually may treat deposits differently.

The tool rounds t × 12 to the nearest whole month for the number of deposits, while growing the original principal for the entered duration. For example, 1.04 years gives 12 deposits, not 12.48 deposits, while principal still grows for 1.04 years. Prefer whole-month durations when comparing a regular monthly plan, and read the account's accrual rules before using a fractional-year projection.

The Savings Calculator uses monthly compounding and rounds the entire projection to whole months. It agrees with the monthly example above for whole-month periods, but fractional-year inputs need not match. A 6% nominal annual rate compounded monthly also has an effective annual growth rate of about 6.1678%; do not substitute an effective annual yield as though it were the same nominal input.

What the projection cannot promise

A constant positive rate is a scenario, not a promised investment return. The calculation excludes fees, taxes, inflation and variable returns. It does not model losses or withdrawals as negative contributions. An account balance and its purchasing power are different quantities.

For the underlying concept, see Investor.gov's definition of compound interest. Its compound interest tool also separates initial investment, contributions, estimated rate and compounding frequency. The examples and timing conventions here were independently checked against OnlineCalMaster's implementation. They are educational estimates, not personalized investment advice.

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