# Thread: Balance to be repaid: cash price $12480; computer bought on hire purchase 1. Originally Posted by richiesmasher Well, the answers in the book are as follows (I) the deposit paid =$3120
(II)the outstanding balance=$9360 (III)the balance to be repaid =$11232
(IV)the hire purchase price=$14352 (V)the difference between the cash price and hire purchase price =$1872

SO let me be as clear as possible.

I read the question, and initally thought it was compound interest, as every month you'd pay off an interest and then take the interest of how much you have left.

But the question specifically says in equal amounts.
The fact that it is paid in equal amounts doesn't prevent it from using compound interest; we get that only from the word "simple" that they used! Ordinary installment loans pay equal amounts, too.

Originally Posted by richiesmasher
SO I thought, ok 18 months equal amounts.

They state simple interest.

SO I used the simple interest formula, my principal being $9360, my rate being 20%, and my time, my time being one month, or in other words 1/18 representing the interest for one month in the alotted time period. SO then I calculated, and worked it out, and got$104 for one month, from here it was just do multiply by 18, which gives me $1872. Now the Balance to be repaid would be the outstanding balance plus the simple interest over the 18 months, which will ultimately give me$9360+$1872 and that gives me$11232.
Based on the answer, the 20% is not an annual rate but a total percentage of interest. I've never heard that done, but I suppose it's literally what the words tell you!

So your calculation for the "balance to be repaid" is simply
balance + 20% of balance = 9360 + 9360 * 0.20 = 9360 + 1872 = 11,232

It could have been calculated merely as a 20% increase over 9360: 9360 * 1.20 = 11,232.

Taking 1/18 only makes sense if you take 20% as the rate for the entire 18 months, not an annual rate. And since you multiplied by 18 anyway, it was not needed at all.

Originally Posted by richiesmasher
ALSO I AGREE WITH YOU GUYS, Soon I will be over with exams, I'm currently preparing for them, these are the types of questions on the exam, but after I will pursue higher education.
Thanks for the tip TK HUNNY multiplying by 0.2 is much better.

Thanks for the proper formats Dennis, I will not ignore that and shove your valuable contributions aside
Peace and love <3
The important thing about 20 vs. 0.2 is that 20% MEANS 20/100 (that is, "%" means "/100"), so that when you wrote 20% ... /100, you were being redundant. You can call it multiplication by 20%, or multiplication by 20 and division by 100, but not both. And just rewriting 20% as 0.20 is easiest.

Now, the remaining question in my mind is, did they actually teach you what they are doing? Have they told you anywhere that "paying simple interest that is equivalent to 20% on the outstanding balance" should be read as "paying 20% of the outstanding balance as interest"? And do they claim this is actually done in business? (You'll have to ask the others about that; I know the math far better than finance or the law.)

And what Denis (and tkhunny at first) were talking about is what would really be done for a typical installment loan, unless perhaps 18-month loans are often done without all that bother.

2. from Investopedia.com

DEFINITION of 'Usury Rate'

A rate of interest that is usually considerably above current market rates. Usury rates are often charged by unsecured lenders on loans. These rates can be illegal in some countries and situations because they often take advantage of unsuspecting individuals.

More from me: Even the relatively benign "Rule of 78s" can get into usury on some loans. ALWAYS read your terms carefully BEFORE signing anything. This is one of the best answers to the obtuse question(s), "What good is math?" or "When will I ever use this?" The bad guys know enough. You can defend yourself against such if you have enough math in your head. Mathematics will save you from very serious errors. I once dominated a national mortgage lending company in a brief dispute we had about escrow payment calculation. Eventually, the company wrote me a very polite note - after they received a threatening letter from a federal agency who could make their lives miserable. Mathematics WILL save you!

3. Originally Posted by Dr.Peterson
Based on the answer, the 20% is not an annual rate but a total percentage of interest. I've never heard that done, but I suppose it's literally what the words tell you!

So your calculation for the "balance to be repaid" is simply
balance + 20% of balance = 9360 + 9360 * 0.20 = 9360 + 1872 = 11,232
Good "catch" Dr P.

Calculating the effective annual rate from that gives 1.9939 per month;
rounded to 2%: 1.02^12 = 1.2682 or 26.82% effective.

4. Originally Posted by Denis
Good "catch" Dr P.

Calculating the effective annual rate from that gives 1.9939 per month;
rounded to 2%: 1.02^12 = 1.2682 or 26.82% effective.
And that's not likely high enough to be illegal. That's just bad credit card. Nowhere near loan-sharking.

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