If a company purchases merchandise on terms of 110 n30 the c

If a company purchases merchandise on terms of 1/10, n/30, the cash discount available is equivalent to what effective annual rate of interest (assuming a 360 day year) ?

(the answer is 18%) I have seen the a formula for this is...        1% x ( 360 days / 20 days ) = 18%

My question is, why is 360 days being divided by the 20 days ? What does this represent or mean ?

Solution

N is number of days after interest free period. For this periods we forgo the discount. Hence, this is the borrowing period and discount rate is the borrowing rate for that period.

Hence, N is 20 days (30-10)