A borrows an amount ₹3,600 from B at a rate of 20% simple interest for 2 years and lends 75% of this amount to C at 20% compound interest for 2 years. A uses the remaining amount for his personal purpose. Find the total loss incurred by A. The amount used for the personal purpose is also considered as a loss.

A borrows an amount ₹3,600 from B at a rate of 20% simple interest for 2 years.

Interest paid by A on the given amount = $$\frac{principal\times rate\times\ time}{100}$$

= $$\frac{3600\times20\times2}{100}$$

= $$36\times20\times2$$

= 1440

lends 75% of this amount to C at 20% compound interest for 2 years.

principal = 75% of ₹3,600

= $$\frac{75}{100}\times3600$$

= ₹2700

Interest received from C = $$principal\left[\left(1+\frac{rate}{100}\right)^{time}\ -1\right]$$

= $$2700\left[\left(1+\frac{20}{100}\right)^2\ -1\right]$$

= $$2700\left[\left(\frac{120}{100}\right)^2\ -1\right]$$

= $$2700\left[\left(\frac{6}{5}\right)^2\ -1\right]$$

= $$2700\left[\frac{36}{25}-1\right]$$

= $$2700\times\ \left[\frac{11}{25}\right]$$

= $$108\times\ 11$$

= 1188

Total loss incurred by A = 1440-1188+amount for his personal purpose

= 1440-1188+25% of ₹3,600

= $$1440-1188+\frac{25}{100}\times3600$$

= $$1440-1188+25\times36$$

= $$1440-1188+900$$

= ₹1152