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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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    @Debanjan Sorry. Was just a bit feeling like Hey, this guy want's us to solve his homework.2011-01-02

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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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    @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