The compound interest earned in two years at 15% per annum is Rs 20640. What is the sum invested (in Rs)?

Let the sum invested = Rs. $$100x$$

Rate of interest = 15% and time period = 2 years

Compound interest = $$P[(1+\frac{r}{100})^t-1]$$

=> $$100x[(1+\frac{15}{100})^2-1]=20640$$

=> $$100x[(\frac{23}{20})^2-1]=20640$$

=> $$100x(\frac{529-400}{400})=20640$$

=> $$\frac{129x}{4}=20640$$

=> $$x=20640 \times \frac{4}{129}$$

=> $$x=160 \times 4=640$$

$$\therefore$$ Sum invested = $$100 \times 640=Rs.$$ $$64,000$$

=> Ans - (A)