As Given
Billing cycle length for a credit card is one calendar month i.e Monthly.
Suppose , Interest for the month of January= $ X
January has 31 days.
Interest for a single Day =$ [tex]\frac{X}{31}[/tex]
Now, if you count the number of days in each month of a year , the minimum number of Days occurs in month of February, whether it is a leap year or Non leap year.(If the period is a month )
So, the Month is February, In which you have to pay lowest periodic interest rate.
