Interest

The principal amount is P, rate of interest is R and time of loan is T

• Simple Interest = $$\dfrac{P*T*R}{100}$$
• Amount = Principal + Simple Interest
• Compound Interest = $$ P(1+\dfrac{R}{100})^{T}$$ - P
• For the same principal, positive rate of interest and time period, the compound interest on the loan is always greater than the simple interest.

If an amount 'P' is borrowed for 'n' years at r% per annum compounded annually, and x is the installment that is paid at the end of each year, starting from the first year, then:

$$P\ =\ \dfrac{\ x}{1+\dfrac{r}{100}}+\ \dfrac{\ x}{\left(1+\dfrac{r}{100}\right)^{^2}}+...+\ \dfrac{\ x}{\left(1+\dfrac{r}{100}\right)^{^n}}$$

or 

$$P\ \left(1+\frac{r}{100}\right)^{n\ }=\ x\ \left(\left(1+\frac{r}{100}\right)^{n-1}+\left(1+\frac{r}{100}\right)^{n-2\ }...\ +1\right)$$

When interest is compounded annually:

A = $$P\left(1+\dfrac{R}{100}\right)^T$$

When interest is compounded half-yearly:

A=$$P\left(1+\dfrac{R}{200}\right)^{2T}$$

When interest is compounded quarterly:

$$A = P\left(1+\dfrac{R}{400}\right)^{4T}$$

For 2 years:

$$CI - SI = P\left(\dfrac{R}{100}\right)^2$$

For 3 years:

$$CI - SI = P\left(\dfrac{R}{100}\right)^2\left(3+\dfrac{R}{100}\right)$$