# Business MathShould money be borrowed to take advantage of a discount?

#### jdrock12

##### New member
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 cant comprehend this subject in-particular. the question is..

#### Deveno

##### Well-known member
MHB Math Scholar
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.

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#### Wilmer

##### In Memoriam
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:

#### chal hat peche

##### New member
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?

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