Practice Compound Interest Questions and Answers 2024

Rule	Description
1	C.I. = \[P\left[\left(1+\frac{r}{100}\right)^n-1\right]\]
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 half-yearly Since r is calculated half-yearly therefore the rate per cent will become half and the time period will become twice, i.e., Rate per cent when interest is paid half-yearly = \[\frac{r}{2}\]% 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 \[S.I.=P\left(\frac{R}{100}\right)^2\] \[C.I.-S.I.=\frac{R\times S.I.}{200}\]
8	Difference between Compound Interest (C.I.) and Simple Interest (S.I.) When T = 3 \[C.I.-S.I.=\frac{PR^2}{10^4}\left(\frac{300+r}{100}\right)\] \[C.I.-S.I.=\frac{S.I.}{3}\left[\left(\frac{R}{100}\right)^2+3\left(\frac{R}{100}\right)\right]\]
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 n₁ yr and y times in n₂ 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 Population after n yr = \[P\left(1+\frac{r}{100}\right)^n\] Population n yr ago = \[\frac{P}{\left(1+\frac{r}{100}\right)^n}\]
12	If the population of a city is P and it decreases with the rate of R% per annum, then Population after n yr = \[P\left(1-\frac{r}{100}\right)^n\] Population n yr ago = \[\frac{P}{\left(1-\frac{r}{100}\right)^n}\]
13	If the rate of growth per year is R₁%, R₂%, R₃%, ......., 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.