Turn an annual rate into a daily amount, accumulate simple interest without early rounding, and distinguish day-count conventions from compounding.
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The calculation
Simple interest = principal × annual rate as a decimal × days ÷ day-count basis
Worked example
At an assumed 7.3% annual rate on an unchanged $10,000 balance and a 365-day basis, daily simple interest is $2. Over 30 days it is $60. A 360-day basis gives about $60.83 over the same 30 days.
The example assumes constant principal and rate with no compounding, payments or fees. Actual accounts follow their agreement, including day-count and rounding conventions.
Video chapters
- 0:00 — How much interest belongs to one day?
- 0:14 — Turn the percentage into a decimal
- 0:32 — Divide the yearly amount by the basis
- 0:47 — Build the 30-day total
- 1:05 — A different basis changes the answer
- 1:22 — Do not round each day too early
- 1:37 — Simple interest and compounding differ
- 1:54 — State the balance, rate, days and basis
Read the full transcript
Suppose an unchanged ten-thousand-dollar balance has an annual interest rate of seven point three percent. Using a three-hundred-sixty-five-day basis, how much simple interest accrues in one day, and in thirty days? We will keep the balance fixed and track the interest separately.
Seven point three percent means seven point three divided by one hundred, or zero point zero seven three. Multiply ten thousand by that decimal. The result is seven hundred thirty dollars for a full year under this simple model. Using seven point three without dividing by one hundred would make the result one hundred times too large.
Now divide seven hundred thirty dollars by three hundred sixty-five. That gives two dollars per day. The units help: dollars for a year divided across the stated days gives a daily amount. The day-count basis is an input to the method, not a detail to assume silently.
Thirty days at two dollars per day produces sixty dollars of simple interest. In one expression, multiply ten thousand by zero point zero seven three, then by thirty, and divide by three hundred sixty-five. The principal remains ten thousand; the accumulated interest sits in a separate total.
Keep the same principal, rate, and thirty actual days, but use a three-hundred-sixty-day basis. The daily amount is about two point zero two seven eight dollars. Carrying the unrounded value gives about sixty dollars and eighty-three cents for the period. The account agreement determines which convention applies.
If a daily calculation contains a fraction of a cent, keep that precision while estimating the period total, then round the final amount. Rounding each daily figure first can produce a different total. A real account may specify its own rounding procedure, so an estimate should state the method it used.
With simple interest on a fixed balance, each day contributes the same amount. With daily compounding, earlier interest joins the balance used for later interest. That creates a growing base. Payments, new charges, changing rates, or fees require additional accounting; multiplying one fixed daily amount is no longer the complete model.
Write the annual rate as a decimal, multiply by the relevant balance, and divide by the agreed day-count basis. For a constant simple-interest period, multiply by the number of days. Our stated example gives two dollars per day and sixty dollars over thirty days, before any other charges.