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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.2011-01-02
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    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.2011-01-02
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    @ FUZxxl: You should get RTFQ award for that comment,the comment seems offensive and hence I am flagging it.2011-01-02
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    @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?2011-01-02
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    @ Ross Millikan: OOPs! I didn't thought of dividing them! Thanks Ross :)2011-01-02
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    @Ross: Thanks a lot,dividing really makes it so easy,I got $5\%$ answer in less than a mint :-)2011-01-02
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    @Debanjan Sorry. Was just a bit feeling like Hey, this guy want's us to solve his homework.2011-01-02

1 Answers 1

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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 ?2011-01-02
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    @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.2011-01-02
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    @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.2011-01-02
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    But `If you are not compounding annually, which magically simplifies things by eliminating the compounding for a one year term` I don't understand could you please explain?2011-01-02
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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.2011-01-02
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    @Ross Millikan: You first have to trigger $\TeX$-Mode by a `$`, and finish it with another. `$150\$$` becomes $150\$.$2011-01-02
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    @FUZxxl: When I did the show source on the problem, I forgot about the dollar signs because there was one. You are right and I have fixed it. Thanks2011-01-02