__
Compound Interest
__

When the interest due at the end of the period becomes a part of the principal and itself earns interest along with the principal, it is called "Compound
interest". Depending upon the length of the interest period, quarterly or so, the formula for compound interest is

S = P *(*1 + i*)*^{n}

Where S = compound interest

Here the factor *(*1 + i*)*^{n }is called compound amount factor or CAF. If interest is paid more than once in a year say semi-annually, quarterly or
monthly etc, the formula for compound amount factor is

$$CAF\ = (1 + \frac{i}{m})^n$$

Where i = interest rate per year

n = no. of years in the period

m = no. of periods per year

##
Compound Interest Examples

**Example 1:**
*Calculate the compound amount when Rs. 2000 are lent at 9% interest arte for 3 years, being compound semi-annually*

**Solution: **

No. of period per year = 2

$$S = p (1 + \frac{i}{m})^n = 2000 (1 + \frac{0.09}{2})^{3 \times 2}$$

2000 *(*1.045*)*^{6} = Rs. 2660 only.

**Example 2:**
*Determine the present value of Rs. 5000 due after 5 years at 9% compound interest rate.*

**Solution:**

$$P = \frac{S}{(1 + i)}^n = \frac{5000}{(1 + 0.00)}^5$$

$$ = \frac{5000}{(1.09)}^5 = 3249.66.$$

The above explains CAF and PWF refer to amount payable in one single payments *(*SP*)*, it should, therefore, be called as CAF *(*SP*)* and PWF *(*SP*)* standing for
*(*1 + i*)*^{n} , $\frac{1}{(1 + i)}^n$ respectively. In most of the cases payments are made in series of periodical 'equal payments'. These are called
'Annuities'.

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