# Suggest quicker method for finding rate percent per annum

$1$.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
@ 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

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?
@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
@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