Simple interest: when to use 360 or 365 days
Count the days, choose the year basis, and find interest and maturity value with a side-by-side example.
AI-assisted writing and calculation checks. Our editorial approach
I = P × r × t
Principal × annual rate × years
The day count and the year basis are separate choices. The same 73 days can mean 73/360 or 73/365 of a year.
Put time and rate in matching units
Simple interest charges interest on the original principal, assuming no partial payments. Start with I = P × r × t, where P is principal, r is the annual rate as a decimal, and t is time in years. The maturity value is M = P + I.
A rate of 8.25% becomes 0.0825. Five months becomes 5/12 of a year. If a question gives days, read its day-count instruction before converting time.
| Convention in this guide | Time in years |
|---|---|
| Ordinary interest, using actual days | Actual days ÷ 360 |
| Exact interest, using a 365-day basis | Actual days ÷ 365 |
These are the conventions used in the supplied chapter. Actual/360 is not the same as 30/360, which also changes how days are counted. Other agreements may specify a different basis, including a leap-year convention. Use the rule stated in the problem.
Count once, then choose the denominator
A $6,400 loan runs from April 9 to June 21, 2026, at 8.25% annual simple interest. Exclude April 9 and include June 21:
- April 10–30: 21 days.
- May: 31 days.
- June 1–21: 21 days.
That is 73 actual days. Choosing a 360-day year does not change this calendar count to 72 or make every month 30 days. It changes the denominator in the next step.
Work the same loan both ways
Ordinary interest:
I = 6,400 × 0.0825 × (73/360) = 107.0666…
Round the final interest to $107.07. The maturity value is $6,507.07.
Exact interest on a 365-day basis:
I = 6,400 × 0.0825 × (73/365) = $105.60
The maturity value is $6,505.60.
The ordinary-interest charge is $1.47 higher after rounding. That direction makes sense: 73/360 is a larger fraction than 73/365. With the same principal, positive rate, and number of days, the smaller year denominator produces more interest.
Keep the fraction in your calculator until the end. Rounding 73/365 to 0.20 happens to be exact here; most day fractions will not terminate so neatly.
What if the term is in months?
For $3,500 at 6.4% annual simple interest for five months, use the stated month term:
I = 3,500 × 0.064 × (5/12) = $93.33, rounded to cents.
M = 3,500 + 93.33 = $3,593.33.
Do not replace five months with an invented number of actual days. If dates and an actual-day convention are supplied instead, calculate the calendar interval.
Before submitting an answer, check three things: the rate is a decimal, time is in years, and the requested result is interest or maturity value. They are different amounts.
Try it yourself
Find ordinary interest and maturity value on $9,200 at 7.5% for 48 actual days, using a 360-day year.
Show the worked answer
I = 9,200 × 0.075 × (48/360) = $92.00. M = 9,200 + 92 = $9,292.00. The time fraction is 48/360, not 48/365 or 48 years.
Keep practicing
Simple interest · Chapter 16References
- Slater, supplied Chapter 16, pp. 425–431
Interest, maturity value, and ordinary versus exact interest. The chapter page ranges are those cited in StudySoda’s supplied reviewer; the original chapter file is not published here.
Original examples for learning. Check the conventions and rounding required by your course.
