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?
On
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: $P(1+\frac R{100})^n-P(1+\frac {nR}{100})$
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.