Simple & Compound Interest

At a glance 11 formulas

1. 1Simple interest$SI = \dfrac{P \times R \times T}{100}$$\text{total interest} = (R \times T)\%\ \text{of } P$
2. 2SI from two amounts$\text{yearly SI} = \dfrac{A_2 - A_1}{T_2 - T_1}$$P = A_1 - T_1 \times \text{yearly SI}$
3. 3n times under SI$R \times T = (n - 1) \times 100$$\text{doubles: } R \times T = 100$
4. 4Compound amount$A = P\left(1 + \dfrac{R}{100}\right)^{n}$$\text{2 years: } CI = \left(2R + \dfrac{R^2}{100}\right)\%\ \text{of } P$
5. 5Half-yearly, quarterly$\text{half-yearly: } \tfrac{R}{2}\%\ \text{for } 2n \text{ periods}$$\text{quarterly: } \tfrac{R}{4}\%\ \text{for } 4n \text{ periods}$
6. 62-year CI minus SI$CI - SI = P\left(\dfrac{R}{100}\right)^{2}$$= \text{one year's SI} \times \dfrac{R}{100}$
7. 73-year CI minus SI$CI - SI = P\left(\dfrac{R}{100}\right)^{2}\left(3 + \dfrac{R}{100}\right)$
8. 8CI amounts in GP$1 + \dfrac{R}{100} = \dfrac{A_{n+1}}{A_n}$$\text{equal gaps: } A_k^{2} = P \times A_{2k}$
9. 9Multiples under CI$n\times \text{ in } T \text{ yrs} \Rightarrow n^{k}\times \text{ in } kT \text{ yrs}$
10. 10Rate on a split (SI)$R = \dfrac{P_1R_1 + P_2R_2}{P_1 + P_2}$$\dfrac{P_1}{P_2} = \dfrac{R_2 - R}{R - R_1}$
11. 11Equal instalments$\text{price} = \dfrac{x}{m} + \dfrac{x}{m^{2}} + \cdots,\ m = 1 + \tfrac{R}{100}$$\text{two instalments: } x = \dfrac{\text{price} \times m^{2}}{m + 1}$