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Formulas of Simple Interest and Compound Interest

Interest

It is the money paid by the borrower to the lender for the use of the money lent.

The sum lent is called the Principal.
Interest is usually calculated at the rate of so many rupees for every year Rs. 100 of the money lent for a year. This is called the rate percent per annum. Per annum means for a year.
The interest is usually paid yearly ( 12 months), half- yearly ( 6 months), Quarterly ( 4 months).

Simple Interest

When interest is calculated on the original price for any length of time it is called Simple Interest (S.I)

Following are the formulas of Simple Interest


$1.S.I=\frac{\Pr incipal\times Rate\times Time}{100}$

$2.\Pr incipal=\frac{100\times S.I}{Rate\times Time}$

$3.Rate=\frac{100\times S.I}{\Pr incipal\times Time}$

$4.Time=\frac{100\times S.I}{\Pr incipal\times Rate}$

$5.Amount=\Pr incipal+S.I$

Compound Interest 

 Money is said to be lent at compound interest when at the end of the year the interest that has become due is not paid to the lender, but is added to the sum lent and the amount thus obtained becomes the principal for the next period. The amount is found out by repeating the process till the last period. Compound Interest is then calculated by taking difference of final amount and original principal.

Following are the formulas of Compound Interest

If Principal = $P , Time = n years, Rate = r% per annum

Case I: When interest is compounded annually :


$Amount=P{{(1+\frac{r}{100})}^{n}}$

Case II: When interest is compounded half-yearly :


$Amount=P{{(1+\frac{r}{200})}^{2n}}$

Case III: When interest is compounded quarterly :


$Amount=P{{(1+\frac{r}{400})}^{4n}}$

Case IV: When rate of interest is different for each year, like r1%, r2%, r3 % for first, second and third year respectively :


$Amount=P(1+\frac{{{r}_{1}}}{100})(1+\frac{{{r}_{2}}}{100})(1+\frac{{{r}_{3}}}{100})$

$C.I=Amount-\Pr incipal$

$C.I=P[{{(1+\frac{r}{100})}^{n}}-1]$



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