Dates might seem simple, but on Exam FM, even a one-day difference can throw off your answer. Learn how consistency in handling beginning- and end-of-month dates can save you time—and costly mistakes—on exam day.
I’m writing this blog on August 27, 2018, the day my third grandchild was born. Dates are important in life. But they’re also important for actuaries, both on the job and when taking exams.
On the surface, managing dates seems easy. It usually only involves finding the time difference between two dates. Since this is basically subtraction—or counting—it feels simple. However, it’s easy to make a small mistake.
And even if you calculate correctly, it’s important to do so efficiently so you don’t waste valuable exam time. If you’re struggling with date problems, perhaps I can help.
Why Consistency Matters
Usually, the goal in working with calendar dates is to count the number of months or years between two points in time.
Let’s assume we need to calculate the number of months between 1/1/2018 and 12/31/2018. We know this is one year, or 12 months, but how would you actually calculate it?
The key is consistency: make sure both dates are in the same format—either both beginning of month (BOM) or both end of month (EOM).
In our example, the first date is BOM and the second is EOM. So, change one to match the other. Let’s change the first date to EOM by adjusting 1/1/2018 to 12/31/2017.
When counting months for the exam, there’s no difference between these two starting points. Even though we moved the first date by one day, both represent a 12-month difference when compared to 12/31/2018.
How to Calculate Months Between Dates
Let’s look at a few examples to see how consistency helps us calculate efficiently.
Example 1
Suppose the two dates are 4/1/2018 and 12/31/2018. The first date is BOM, and the second is EOM. To make them consistent, change the first date to 3/31/2018 (EOM).
Now both are EOM, and we can simply subtract months:
12 – 3 = 9.
If we hadn’t changed the first date, we’d subtract 4 from 12, which would be wrong because the two dates weren’t expressed in the same format.
Example 2
Alternatively, we can make both dates BOM instead. Change 12/31/2018 (EOM) to 1/1/2019 (BOM). Think of January 2019 as the 13th month of 2018.
Now subtract:
13 – 4 = 9.
In general, if the second date is one year after the first (for example, 2019 vs. 2018), add 12 months to the month of the second date before subtracting the difference.
Example 3
How many months are between 4/1/2018 and 1/31/2019? The first date is BOM, and the second is EOM. Change the second date to BOM—2/1/2019.
There’s a one-year difference, so:
2 + 12 – 4 = 10 months.
If the second date were 1/31/2020, there’d be a two-year difference. So:
2 + (2 × 12) – 4 = 22 months.
To summarize, here’s a simple process for date calculations:
- Step 1: Express both dates in the same format—either both EOM or both BOM.
- Step 2: If the second date is in a later year, add 12 months for each additional year.
- Step 3: Subtract the months after adjusting in Steps 1 and 2.
The result is the number of months between the two dates.
One Final Thought
You may be wondering if we can always convert between EOM and BOM. For example, is there ever a time when we shouldn’t convert April 1 to March 31—or April 30 to May 1?
As mentioned before, if the purpose is calculating interest between dates, this conversion is safe. The only time you need to be careful is when you’re determining whether a cash flow occurs within a specific time period.
Let’s say you’re given a savings fund and you’re calculating the balance as of 12/31/2018. If there’s a deposit on 1/1/2019, you can treat that as 12/31/2018 when calculating interest. However, since the deposit happens one day after the valuation date, you should not include it in the accumulated savings as of 12/31/2018.
The key takeaway is that converting between BOM and EOM should never affect whether a cash flow occurs within the valuation period.
Extending the Concept
This same principle applies to other time periods, such as quarters or years.
For example, how many years are there between 1/1/2008 and 12/31/2018?
The first date is the beginning of the year (BOY), and the second is the end of the year (EOY). To make them consistent, change 1/1/2008 to 12/31/2007.
Now both are EOY, so you can subtract:
2018 – 2007 = 11 years.
Working with dates is a common issue on Exam FM, and you may see it on other exams too, though less often. So, I recommend incorporating these concepts into your exam prep as soon as possible.