Expert: Abe Mantell - 12/30/2010

Question
Hello:

I read about this method in an old business mathematics book and was curious about how it works to produce the correct answer.

"Percent-day method is based on 360 days‚ time and 1% interest. Any interest rate multiplied by any number of days is equal to so many %-days."
Example: 82 days at 5% equals 410%-days.

"The rest of the calculation to find interest using his method involves multiplying the amount of interest at 1% by the ratio of %-days to 360."

Here is an example calculation: $720 for 92 days at 7% = 7% X 92 days = 644%-days.

644/360 X $7.20(1% for 360 days) = $12.88

Why is the (1% for 360 days) placed in this calculation as shown above? I think that the day units would cancel from the 644-days/360 days.
Is the percent from the 644%-days removed from the 644 and placed here to represent the interest on $720 X 1/100 X 1/360?
This would equal $7.20.

I thank you for your reply.

Answer
Hello Kenneth,

The "correct" and simplest way to do it and think about is:
$720 x 7% x 92/360 = $12.88

Here's why.  $720 x 7% gives the annual interest amount, then
multiplying by 92/360 gives the fractional part of the year
for which interest is being charged.

The calculation you showed is equivalent.  You did 92 x 7 then
divided by 360 then multiplied by 1%.  The multiplication by 1%
really converts the 644 to a percentage...you could have obtained
the same answer if you wrote 644% as 6.44...see?

Abe