Math CentralQuandaries & Queries


Question from Kenneth:


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

Can you explain the logic of this calculation? I can understand that days multiplied by percent equals %-days, but I do not understand how $\$720$ becomes $\$7.20$ and why is (1% for 360 days) used?

In other words, why does the method involve multiplying the amount of interest at 1% by the ratio of %-days to 360?

What became of the 92 days?

I thank you for your reply.


For the example you give of $\$720$ for 92 days at 7% based on 360 days the conventional calculation would be to find 7% of $\$720,$ which would be for 360 days and then multiply by 92/360 since you only used 92 of the 360 days. This would give


In the percent-day method the multiply the 7 and 92 first


to get


Since $\$720/100 = \$7.20$ the resulting calculation is $\frac{644}{360} \times \$7.20 = \$12.88.$

I hope this helps,

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