Counting

The correct way to count days for money saved

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

18 October 2015

Kimathi Mwirichia insists that I made a mistake when counting the days in last week’s article. He says that “the number of days from 3rd to 30th of September is 28 and not 27 as you have indicated. When you want to avoid making a mistake it is advisable to subtract the two numbers and add one: hence 30-3+1=28… [therefore] the returns that you calculated need adjustment to factor in the extra day.”

I engaged him Kimathi in an email discussion and I was not able to convince him that I was right. My argument was based on this question: if you lend me money today [18th] and I return it to you tomorrow [19th], how many days have I kept it?

Kimathi insists it is two days [the 18^th and the 19^th], while I say it is one day. What do you think dear reader?

If you say it is two days, then I will ask a second question: if you lend me the money today and we agree that I should keep it for one day, when should I return it? Kimathi did not answer that question! Instead, he pointed out that “When we talk of a date…we mean a full day and not part thereof.”

Let me now try a different approach: Last week I discussed the case of Robert Mutemi who deposited Sh10,000 on 3^rd September and then added Sh20,000 on the 15^th and another Sh100,000 on the 25^th. The question for Kimathi is: what amount should be used for calculating interest on the 15^th?

You see; when the day started, there was Sh10,000, then sometime during the day, it changed to Sh30,000. Which of these two amounts should the fund manager use?

If Kimathi says Sh10,000, then we must recognise that he is using the day’s opening balance. And so, we must apply the same logic for the 3^rd September; that is, opening balance was zero. The Sh10,000 was an opening balance from the 4^th to the 15^th. Now let’s count those days: 4^th September is day-1; 5^th is day-2; 6^th is day-3;…15^th is day-12.

If, on the other hand, Kimathi says that the balance for calculating interest on 15^th September is Sh30,000, then we recognise that he is using the closing balance. We apply the same logic to 3^rd September: the closing balance was Sh10,000. This situation remained all the way up to the 14^th. Remember that on the 15^th it changed to Sh30,000.

So, we count the days as before: 3^rd September is now day-1; 4^th is day-2; 5^th is day-3…and 14^th is day-12. The answer is the same as before!

Now this might look like a trivial exercise, but, as Kimathi points out, a one day mistake can result in a major loss for a bank (by undercharging) of a customer (by overcharging). In deed, the matter of counting days is so important that even our constitution sees it fit to clearly define it; it says in Article 259(5)(a) “In calculating time between two events for any purpose under this Constitution, if the time is expressed as days, the day on which the first event occurs shall be excluded, and the day by which the last event may occur shall be included”