As a hypothetical example, you invest 100 million yen at 2% from March 15 to August 31, 2026, and round the interest to the nearest yen. If the day count convention is Act/360, how much is the interest?
Quiz: Dates and Day Counts
Last reviewed: September 24, 2026
This is a draft, shown for review before publication.
4 questions to check your understanding of the chapter “Dates and Day Counts”. Choose an answer and select “Check answer” to see the answer and explanation. You can also open “Answer and explanation” to see the answer first.
Question 1
Answer and explanation
Answer: B
Act/360 counts the actual number of days in the period and divides by 360 to convert it into years. The days in the period are counted including the start date and excluding the end date. That gives 17 days in March (the 15th to the 31st), 30, 31, 30, and 31 days in April to July, and 30 days in August (the 1st to the 30th), for a total of 169 days. The interest is 100 million yen × 2% × 169 ÷ 360, which is 938,889 yen.
926,027 yen is the interest under Act/365F, which divides the same 169 days by 365. 922,222 yen is the interest under 30/360, which treats each month as 30 days and counts 166 days, and 916,667 yen is the interest under 30E/360, which counts 165 days. This period has 169 days, which Act/360 divides by 360, so it gives the most interest.
Learn more: Day Count Conventions
Question 2
As a hypothetical example, you calculate the interest on 100 million yen at 2% for the month from February 15 to March 15, 2026, rounding to the nearest yen. Which gives more interest, Act/360 or 30/360?
Answer and explanation
Answer: C
This month has 28 actual days, but 30/360 counts 30 days. The interest is 166,667 yen under 30/360 and 155,556 yen under Act/360, so 30/360 gives more. The reason is that February has fewer actual days (28, or 29 in a leap year) than 30. 30E/360 also counts this period as 30 days, and its interest is 166,667 yen, the same as 30/360.
If you assume that Act/360 always gives the most interest, you would choose Act/360. However, a period with many 31-day months has more actual days than days counted at 30 per month, and that is when Act/360 gives more interest than 30/360. Which convention gives more interest changes with the months the period covers. "Both give the same" does not apply, because the actual days and the days counted at 30 per month differ for this period.
Learn more: Day Count Conventions
Question 3
The scheduled interest payment date is December 31, 2026 (Thursday), and the Tokyo calendar is used. If the business day convention is Modified Following, on what date is the payment made?
Answer and explanation
Answer: B
Under Modified Following, the payment is made on December 30, 2026 (Wednesday). Tokyo holidays are the bank holidays in Japan: Sundays, Saturdays, holidays under the Act on National Holidays, and December 31 to January 3. December 31 is not a national holiday and falls on a Thursday in 2026, but it is a bank holiday, so the scheduled date moves. Modified Following moves the scheduled date to the next business day. However, if that day falls in the next month, it moves the date to the immediately preceding business day instead. The next business day, January 4, 2027 (Monday), falls in the next month (and the next year), so the date moves to the preceding business day, December 30 (Wednesday).
January 4, 2027 (Monday) is the result under Following, which moves the date to the next business day. Keeping December 31 (Thursday) is the mistake of assuming that every weekday is a business day.
Learn more: Business Day Conventions and Holiday Calendars
Question 4
As a hypothetical example, you calculate the interest on a notional amount of 10 billion yen at a fixed rate of 1% from July 31, 2026 (Friday), to the scheduled date of October 31 (Saturday). The interest uses actual days divided by 365 and is rounded to the nearest yen. If the Following convention moves the payment date and the end of the period to November 2 (Monday), how does the interest compare with counting to the scheduled date?
Answer and explanation
Answer: A
Moving the end of the period from October 31 to November 2 lengthens the period by 2 days, from 92 to 94. Counting to the scheduled date, the interest is 100 million yen × 92 ÷ 365, or 25,205,479 yen. Counting to November 2, it is 100 million yen × 94 ÷ 365, or 25,753,425 yen, which is 547,946 yen more. One year of interest is 1% of 10 billion yen, or 100 million yen. One day of interest is 100 million yen ÷ 365, about 274,000 yen, and the difference is two days' worth.
273,973 yen more is what you get if you count the period as longer by only one day (100 million yen ÷ 365 = 273,972.6 yen). There are 2 days from October 31 (Saturday) to November 2 (Monday). 821,918 yen more is what you get if you count 3 more days, through the end date of November 2, and calculate with 95 days. The end date is not counted. 547,946 yen less is what you get if you read the longer period the wrong way round. The period gets longer, so the interest increases.
Learn more: Business Day Conventions and Holiday Calendars