Rule  Description 

1 
C.I. = \[P\left[\left(1+\frac{r}{100}\right)^n1\right]\] 
2 
Amount (A) = \[P\left(1+\frac{r}{100}\right)^n\] 
3 
If rate of compound interest differs from year to year, then Amount (A) = \[P\left(1+\frac{r_1}{100}\right)\left(1+\frac{r_2}{100}\right)\left(1+\frac{r_3}{100}\right).....\] 
4 
Compound interest – when interest is compounded annually but time is in fraction If time = \[t \frac{p}{q}\] years, then \[P\left(1+\frac{r}{100}\right)^t\left(1+\frac{\frac{p}{q}r}{100}\right)\] 
5 
Compound interest – when interest is calculated halfyearly Since r is calculated halfyearly therefore the rate per cent will become half and the time period will become twice, i.e., Rate per cent when interest is paid halfyearly = \[\frac{r}{2}\]% Time = \[2 \times \text{time given in years}\] Hence, Amount (A) = \[P\left(1+\frac{r}{200}\right)^{2n}\] 
6 
Compound interest – when interest is calculated quarterly Since 1 year has 4 quarters, therefore rate of interest will become \[\frac{1}{3}th\] of the rate of interest per annum, and the time period will be 4 times the time given in years, Hence, for quarterly interest Amount (A) = \[P\left(1+\frac{r}{400}\right)^{4n}\] 
7  Difference between Compound Interest (C.I.) and Simple Interest (S.I.) When T = 2

8  Difference between Compound Interest (C.I.) and Simple Interest (S.I.) When T = 3

9  NOTE: SI and CI for one year on the same sum and at same rate are equal. 
10  If a certain sum at compound interest becomes x times in n_{1} yr and y times in n_{2} yr, then \[x^{\frac{1}{n_1}}=y^{\frac{1}{n_2}}\] 
11  If the population of a city is P and it increases with the rate of R% per annum, then

12  If the population of a city is P and it decreases with the rate of R% per annum, then

13  If the rate of growth per year is R_{1}%, R_{2}%, R_{3}%, ......., R_{n}%, then Population after n yr = \[P\left(1+\frac{R_1}{100}\right)\left(1+\frac{R_2}{100}\right)\left(1+\frac{R_3}{100}\right).....\left(1+\frac{R_n}{100}\right)\] NOTE: This formula can also be used, if there is increase/decrease in the price of an article. 