Borrowing Money to take a cash discount

[ctsfish]

My problem states: Janet bought a printer that had a list price of $600 with a $100 trade discount with 2/10, n/30 terms. Janet didn't have the money so she decided to get a bank loan @ 8% to take advantage of the cash discount. How much would Janet save (assume 360 days) The book answer: a savings of $7.82

I am having trouble arriving at this answer.

1) 600.00 x .98 (2% discount) = $588.00 less the $100.00 trade discount (not subject to 2%) = $488.00 total cost
2)$488 x .08 x 1(year or 360 days ordinary interst) = 39.04 interest plus $488.00 = $527.04
Any suggestions on how to get to the $7.82 answer?

 

[Deleted member 4993]

My problem states: Janet bought a printer that had a list price of $600 with a $100 trade discount with 2/10, n/30 terms. Janet didn't have the money so she decided to get a bank loan @ 8% to take advantage of the cash discount. How much would Janet save (assume 360 days) The book answer: a savings of $7.82

I am having trouble arriving at this answer.

1) 600.00 x .98 (2% discount) = $588.00 less the $100.00 trade discount (not subject to 2%) = $488.00 total cost
2)$488 x .08 x 1(year or 360 days ordinary interst) = 39.04 interest plus $488.00 = $527.04
Any suggestions on how to get to the $7.82 answer?

Since the list price was applicable for net 30, I think you need to calculate interest for 30 days - compounded daily.

Then - I think is discounting is applied after trade in (price paid = 490)

490*(1 + .08/360)^30 = 493.2772145

488*(1 + .08/360)^30 = 491.2638381

(500 - either of the above ) does not equal to 7.82.

Sir Denis .... Sir Jonah .... where art thou!!!

 

[ctsfish]

Thanks but tries that. First rule of thumb trade discounts are not applicable to other discounts.

What i had done originally was take 488 x.08 x 30/360 =3.25????

 

[Denis]

Sir Denis rides in to the rescue, beating Sir Jonah to the tower....

The invoice is for 600 - 100 = 500
The discount = 500(.02) = 10
So Janet pays 490 AFTER 10 DAYS; needs to borrow 490 for 20 days.

.08 / 360 * 20 * 490 = 2.18 : Janet borrows 490 for 20 days
10 - 2.18 = 7.82

What happens after (whether she pays loan on time or not ....) matters not!

 

[ctsfish]

Thank you sir denis. I was close but no cigar. makes perfectectly good sense

 

[Deleted member 4993]

Thanks but tries that.

First rule of thumb
trade discounts are not applicable to other discounts.

Sir Denis rides in to the rescue, beating Sir Jonah to the tower....

The invoice is for 600 - 100 = 500
The discount = 500(.02) = 10

So then the rule-of-thumb does not apply to the "correct" answer....

Cut that thumb out.....

What i had done originally was take 488 x.08 x 30/360 =3.25????