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If principal, time and rate are given how,do I find the difference between Compound interest and Simple Interest?

p=12,000 n=1 and a  1/2 yrs. r=10% per year 

Formulae that I know:

CI - SI for 2 years = P(R/100)^2 CI-SI for 3 years = P(R/100)^2 (R/100 + 3) 

But none of these will work for 1 and a half years, so what formula do I use? Or how do I use these formulae in this context?

3 Answers 3

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Formula for simple interest:

$P_{SI} = P \left(1 + \frac{nR}{100}\right)$

Formula for compound interest:

$P_{CI} = P \left( 1+\frac{R}{100} \right)^n$

Therefore their difference is

$P_{CI} - P_{SI} = P \left( \left(1+\frac{R}{100}\right)^n - \left(1+\frac{nR}{100}\right)\right)$

If you substitute $n=2$ and $n=3$ into this formula, and expand out the brackets, you will get the formula you quoted in your question.

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    alright, thanks2012-07-26
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The general compound interest formula says that after $n$ terms at a rate of $R$ percent per term is that the final principal is $P(1+\frac R{100})^n$. Often $R$ is quoted as an annual rate, but if you compound monthly you need to use $\frac R{12}$ per month and $n$ is the number of months. If you have partial terms, you need to specify what happens for a partial term. Maybe you get nothing for the last half year, maybe you get half the interest, or whatever. For simple interest, the final principal is $P(1+\frac {nR}{100})$, so the difference is just the difference of these: $P(1+\frac R{100})^n-P(1+\frac {nR}{100})$

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    @Nirvan: So when you have a half year, how much interest do you get? Your formulas, as you say, are specific to 2 or 3 periods. Chris and I have given you equivalent formulations for any number of periods.2012-07-26
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The answer is simple: First find S.I.(You should be knowing how to). Then for C.I. : Find C.I. For the whole no part of time period(1 in this case). Then find S.I. for half year using the Principal as Amount obtained in previous step(13200 in this case). Then add the C.I. Of first step and S.I. Of second step.(C.I.= 1200 and S.I.=660) Thus total C.I. is 1860. Therefore the difference is C.I. - S.I = 1860-1800 = 60