#### notes

Suppose `P_1` is the sum on which interest is compounded annually at a rate of R % per annum.

Let `P_1` = ` 5000 and R = 5. Then by the steps mentioned

1. `SI_1 = Rs.(5000 xx 5 xx 1)/100 ` so, `A_1 = Rs. 5000 + (5000 xx 5 xx 1)/100` = `Rs.5000 (1+5/100)=P_2` |
Or `SI_1= Rs.(P_1 xx R xx 1 )/100` Or `A_1=P_1 + SI_1 = P_1 + (P_1R)/100` = `P_1(1+R/100) xx R/10 =P_2` |

2. `SI_2 =Rs.5000(1+5/100)xx (5xx1)/100` `=Rs.(5000 xx 5)/100 (1+5/100)`
`Rs.5000(1+5/100)(1+5/100)` `Rs. 5000 (1+5/100)^2 = P_3` |
or `SI_2 = (P_2xx Rxx1)/100` `=P_1(1+R/100) xx R/100` `=(P_1R)/100 (1+R/100)` `A_2 = P_2 + SI_2` `=P_1(1+R/100)+P_1R/100(1+R/100)` `=P_1(1+R/100)(1+R/100)` `=P_1(1+R/100)^2 = P_3` |

The amount at the end of n years will be

`A_n = P_1(1+R/100)^n` Or we can say

A = `P(1+R/100)^n`