AFCAT Model Paper 4

Given: Compound interest for 2 years = Rs. 2050 Simple interest for 3 years = Rs. 3000 Formula Used: For compound interest $A = P\left(1+\frac{r}{100}\right)^t$, Where, $P=$ Principal, $r=$ Rate, $t=$ Time For simple interest $I = \frac{(P \times r \times t)}{100}$, Where $I=$ interest Calculation: According to the question $2050 = P\left(1+\frac{R}{100}\right)^2 - P$ ----(i) And, $3000 = \frac{(P \times R \times 3)}{100}$ ⇒ PR = 100000 ----(ii) Dividing (1) by (2), we get $\frac{PR}{P\left(1+\frac{R}{100}\right)^2 - P} = \frac{100000}{2050}$ ⇒ $2050 R = 100000\left(1 + \frac{R^2}{10000} + \frac{R}{50} - 1\right)$ ⇒ 2050R $= 10R^2$ + 2000R ⇒ R = 5% Substituting in equation (ii) we get, ⇒ P × 5 = 100000 ∴ P = Rs. 20000