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$1$.The compound interest on certain sum for $2$ years is $\$410$ and simple interest is $\$400$. Find the rate of interest per-year.

$2$.A sum of money invested at compound interest amounts in 3 years to $\$ 2400$ an in $4$ years to $ \$ 2520$. Find the rate of interest per-year.

Solving them using the traditional compound interest formulas is a bit tedious for me under exam conditions,so please suggest if there is any kind of short-cut procedure to solve them.

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Maybe you should first show how you did it, then we can see if anything can be simplified. –  Raskolnikov Jan 2 '11 at 11:49
    
Using the standard compound interest and simple interest formulas and forming equations,but as in the compound interest formula there is a term exponential of $4$ which makes things a bit complex. –  Quixotic Jan 2 '11 at 11:51
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@ FUZxxl: You should get RTFQ award for that comment,the comment seems offensive and hence I am flagging it. –  Quixotic Jan 2 '11 at 11:54
    
@Debanjan: yes there is an exponential of 4, but I think there is an exponential of 3 as well and they will divide out. Am I correct? –  Ross Millikan Jan 2 '11 at 12:02
    
@ Ross Millikan: OOPs! I didn't thought of dividing them! Thanks Ross :) –  Quixotic Jan 2 '11 at 12:04

1 Answer 1

up vote 2 down vote accepted

For 1, the difference between compound interest and simple interest is that you pay interest on the interest. So if you are compounding annually, you have $\$10$ interest on $\$400$ in one year. So the interest rate is what?

For 2, again if you are compounding annually, you have $\$120$ interest on $\$2400$. So the interest rate is what?

If you are not compounding annually, which magically simplifies things by eliminating the compounding for a one year term, I don't see any easy way. If you have a spreadsheet that has a goal seek, you can use that.

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@Ross Millikan: Is it just for me or there is some problem in formatting in this answer ? –  Quixotic Jan 2 '11 at 12:09
    
@Debanjan: When I used dollar signs, it read them as putting into $TeX$. So I checked your question and you escaped them with backslashes. I tried that. It seems not to work. But I thought it was readable enough, so I gave up. Maybe the fact that you boldfaced things is the difference. –  Ross Millikan Jan 2 '11 at 12:12
    
@Ross Millikan:Formatting or no formatting I do like this answer precisely the difference between compound interest and simple interest is that you pay interest on the interest. You make things pretty much easy.Thanks. –  Quixotic Jan 2 '11 at 12:25
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@Debanjan: Compounding annually over one year (or any period) is the same as simple interest over one year (or the same period) because the interest is paid at the end of the term and there is no more time to accrue interest on the interest. So you can use the simple interest formula instead of the (more complicated) compound interest formula. –  Ross Millikan Jan 2 '11 at 12:31
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@Ross Millikan: You first have to trigger $\TeX$-Mode by a $, and finish it with another. $150\$$ becomes $150\$.$ –  FUZxxl Jan 2 '11 at 12:52

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