There is 75% increase in an amount in 5 years at simple interest. What will be the compound interest of Rs 40000 after 2 years at the same rate?

Let the rate of interest = $$r$$%

Let sum invested under simple interest = Rs. $$100x$$ and time period = 5 years

=> Interest earned = $$\frac{75}{100} \times 100x = Rs. 75x$$

Simple interest = $$\frac{P \times R \times T}{100}$$

=> $$\frac{100x \times r \times 5}{100} = 75x$$

=> $$r = \frac{75}{5} = 15\%$$

Sum invested under compound interest = Rs. 40,000 and time period = 2 years

=> Compound interest = $$P[(1 + \frac{R}{100})^T - 1]$$

= $$40,000 [(1 + \frac{15}{100})^2 - 1]$$

= $$40,000 [(\frac{23}{20})^2 - 1] = 40,000 (\frac{529 - 400}{400})$$

= $$100 \times 129 = Rs. 12,900$$