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June 20th, 2011, 09:03 AM   #1
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I'm a parent going back to school

Can someone please help me break this down?

I have the answer key but would like someone to show me how it's done please and thank you.

What is the simple interest of $1500.00 for 4 months at 6 3/4% annual interest?
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June 20th, 2011, 09:10 AM   #2
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Re: I'm a parent going back to school

The annual interest is 6.75%, thus 4 months interest must be 4/12 = 1/3 of that, i.e. 2.25%. Now take 2.25% of your principal amount.
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June 21st, 2011, 02:18 AM   #3
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Re: I'm a parent going back to school

For future reference, since all your numbers won't fall out as neatly as this one does, the "proper" basic interest formula is:
principal x rate x time.

Hence:


Granted, that math is going to come out exactly the same. But, because not all interest rates will divide so neatly, and also to avoid some rounding issues that can come up, I would suggest using this method and putting into your calculator in this order, doing the multiplications first, and that division of 12 last. And just keep everything in your calculator as you go. (In certain instances, doing this in this manner can avoid ending up with 4999.999999 and other weird looking things.)

Also note that if it's quoted as months, keep in months (out of 12). If it's given in days, like 30 days, 90 days, whatever, then keep it in days, and divide by 360 or 365, whichever you're instructed to do. Point being, don't turn months into days and vice versa. That can sometimes work, but sometimes not.

And congrats on going back to school. I think this is getting more common, but the school where I work, for many, many years we've commonly gotten older students, with kids and full-time jobs, etc.
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June 21st, 2011, 11:18 AM   #4
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As touched on above, there tend to be hidden assumptions in respect of interest calculations that mathematics textbooks tend to gloss over (but accountancy textbooks would explain). For this problem, the solution given above assumed (without adequate grounds, really) that the interest would be the same for each month, but four consecutive months are not exactly one third of a year.
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June 21st, 2011, 09:36 PM   #5
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Re: I'm a parent going back to school

As a general rule, if the term is given as months, it's done as equal months. I have seen that in accounting books, business math books, and algebra books. The (mostly justified) assumption is based both on that fact, and the fact that nothing about dates was provided, without which you could never convert it to days, nor would you know whether 360 or 365 days should be used. Granted, people leave stuff out of problems, and sometimes assumptions are in the body of the chapter and not given in instructions. But I have yet to see a textbook take something given in months and convert it into days. If they want days, they generally give the term in days, like 90 days (which isn't 3 months). Doesn't mean something else can't exist, but that's just the way I've always seen it.

I could see maybe a finance or banking textbook getting picky about the number of days in those four months.
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June 22nd, 2011, 05:42 AM   #6
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Does the textbook you're using deal with these issues, newphorik?
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June 22nd, 2011, 01:56 PM   #7
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Re: I'm a parent going back to school

I'm pretty sure we can assume months as direct fractions of a year for which the interest is quoted - we are considering simple interest. Thus it would make little sense to deal with specific day count conventions as the impact would be insignificant compared to dealing with compounding for instance - if things were to get more realistic.
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June 22nd, 2011, 06:30 PM   #8
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If two amounts (under $50) differ by n%, for what maximum value of n would you describe their difference as insignificant?

Without doing the arithmetic that would be needed to calculate the interest accurately, put in order of preference:

(a) interest for four months from today, compounded monthly at a monthly rate of 0.5458% (1.005458^12 ? 1.0675),
(b) interest for four months from today, calculated as simple interest of 2.25% for the period, or
(c) interest for 122 days, calculated as simple interest of 6.75/365 % per day?

Without doing the arithmetic, how much difference (giving specific estimated (or guessed) amounts, not just a phrase such as "not much" or "very little") do you think there would be between the interest amounts for the three alternatives?
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June 23rd, 2011, 01:27 AM   #9
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Re: I'm a parent going back to school

skipjack, don't get me wrong - I know it matters in practice - a lot. But the assignment did not really seem like one where we consider details (based on the simple interest part of the question), which there can be quite enough of in practice.
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June 23rd, 2011, 02:06 AM   #10
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The question was probably intended to test basic knowledge of how simple interest is found (or estimated). I was exploring beyond that.
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