Should money be borrowed to take advantage of a discount?

[jdrock12]

Okay so I'm trying to figure out how to do this example problem and if someone can solve it for me and show the work it would be awesome. My professor is great but i can't comprehend this subject in-particular. the question is..

"You are the accountant for Leather City, a retail furniture store. Recently, an order of sofas and chairs was received from a manufacturer with terms of 3/15,n/45. The order amounted to $230,000. They do not have sufficient cash on hand to take advantage of the discount. Leather City can borrow the money at 13% interest.

Would it be worthwhile to borrow money for 30 days in order to pay the bill within the discount period? why? Be specific. Justify your answer in terms of dollars"

 

[MarkFL]

Re: Having some diffuculties answering this question if anyone can help me solve it.

Hello jdrock12,

We typically do not provide full solutions to problems. Our goal is to help by offering hints and suggestions so that the student is engaged in coming to the solution, and learns a great deal more this way.

I am confused by the phrase "with terms of 3/15,n/45." Can you explain what this means and show what you have tried so far?

edit: I changed the title of the topic to give a brief description of the problem.

 

[jdrock12]

hey sorry about that and the terms "3/15 n/45" means you will get a 3 percent discount if the amount due is payed within 15 days and they want the full amount no matter what in 45 days.

 

[MarkFL]

How much of the order needs to be financed?

Let's assume the entire \$230000 is to be borrowed at 13% APR. How much will have to be repaid to the lender after 30 days?

 

[Deveno]

Umm,no...the purpose of borrowing the money is to obtain the 3% discount, so they only have to borrow $\$223,100$.

The question is thus: will the interest on the 30-day loan be more than 6,900 dollars?

Unfortunately, this depends on what the 13% interest MEANS. Is it an APR (annual percentage rate), or a flat one-time fee, and how often is it compounded, if it is an APR?

We do not know these things, which makes this problem currently unsolvable.

Worst case scenario: it is a flat fee, in which case the loan is a VERY bad idea (as it costs $29,003 to obtain the money, which more than offsets the 3% discount).

Two likely scenarios:

a) the interest is an APR, compounded monthly (this is easy to figure out).

b) the interest is an APR, compounded continuously (this is slightly more complicated).

I won't give away the answer here, but I will note that the continual compounding rate yields an answer that is only pennies away from compounding daily (assuming 365 days in a year).

The terms 3/15, n/45 are a bit more generous than usual, most utilities use net 30 billing, and many businesses use net 10 billing (with fees and/or collection proceedings initiated for past-due accounts). Perhaps the manufacturer is allotting 2 weeks for delivery, which counts against the payment period.

 

[Wilmer]

Keeping it simple:

230000 * .03 = 6900

Discount is 15 days, not 30 days; so borrow for 15 days:
230000 * .13 / * (15 / 360) = ~1245

Anyway, if loan MUST be for 30 days, then 2490:
still way ahead

 

[chal hat peche]

I am confused by the phrase
"with terms of 3/15,n/45." Can you explain what this means and show what you have tried so far?__________________________________
Arslan1