Kearns, Inc., sells its goods w/ terms of 1/20, net 50: cost of trade credit?

[Trickster]

Kearns, Inc., sells it's goods with terms of 1/20, net 50. What is the cost of the trade credit?

I answered this problem by doing this:

Credit terms = 1/20, net 50

Formula: Ear = (1 + discount/discounted price)^365/days credit - 1

Ear = (1+ 1/99)^365(50-20)

Ear = (1 + 0.010)^365/30 = (1.01)^12.16 = the answer I get is 1.128


The problem I'm having with this is the answer key is showing me the anser is "13.01%" It seems I'm doing something wrong with the calculations but I don't know what. Got Finals tomorrow and this is the last problem I'm struggling with so any help is appreciated.

 

[Ishuda]

Kearns, Inc., sells it's goods with terms of 1/20, net 50. What is the cost of the trade credit?

I answered this problem by doing this:

Credit terms = 1/20, net 50

Formula: Ear = (1 + discount/discounted price)^365/days credit - 1

Ear = (1+ 1/99)^365(50-20)

Ear = (1 + 0.010)^365/30 = (1.01)^12.16 = the answer I get is 1.128


The problem I'm having with this is the answer key is showing me the anser is "13.01%" It seems I'm doing something wrong with the calculations but I don't know what. Got Finals tomorrow and this is the last problem I'm struggling with so any help is appreciated.

I assume [but be careful of that word, it has implications for u & me], that what you mean is that the bill is due and payable in 50 days but if you pay the bill within 20 days, you can take a 1% in the bill but if you wait the full 50 days you pay the full amount [1% reduction if within 20 days, otherwise full amount (net) and you have 50 days to pay = 1/20, net 50].

Knowing the answer and working backwards we get the following example: Suppose the bill were $100. Then, if you pay the bill at the end of 20 days, you pay $99. If you pay at the end of 50 days you pay $100. If you do pay at the end of 20 days, you get interest of $1 on the $99 you paid for 30 days as compared to if you had paid at the end of 50 days. So
Interest amount = 1/99 ~ 1.0101%
Periods in year = 365/30 ~ 12.167
Factor for amount earned in 1 year = (1+Interest amount)^Periods ~ 1.010101^12.167 ~ 1.1301
Effective Annual Interest ~ 13.01%