Raja borrowed ₹15,000 on simple interest at the rate of 13% per annum and lent it on compound interest at the rate of 15% per annum, compounded annually. What is Raja's gain in two years?

Raja borrowed ₹15,000 on simple interest at the rate of 13% per annum.

Simple interest for two years = $$\frac{principal\times\ rate\times\ time}{100}$$

= $$\frac{15000\times13\times2}{100}$$

= $$150\times26$$

= 3900    Eq.(i)

lent the same money on compound interest at the rate of 15% per annum, compounded annually

compound interest for two years = $$principal\left[\left(1+\frac{rate}{100}\right)^{time}\ -\ 1\right]$$

= $$15000\left[\left(1+\frac{15}{100}\right)^2\ -\ 1\right]$$

= $$15000\left[\left(\frac{115}{100}\right)^2\ -\ 1\right]$$

= $$15000\left[\left(1.15\right)^2\ -\ 1\right]$$

= $$15000\left[1.3225\ -\ 1\right]$$

= $$15000\times0.3225$$

= 4837.5    Eq.(ii)

Raja's gain in two years = Eq.(ii)-Eq.(i)

= 4837.5-3900

= ₹937.5