A borrowed a sum of Rs. 4000 from B at the rate of 10% per annum under simple interest. Immediately A gave this money to C at the same rate under compound interest compounded quarterly. Find the profit of A in doing so after 6 months.

Explanation

Principal, P=Rs. 4000
Rate of Interest, R=10%
Time period =6 months `=(1)/(2)` year
Amount paid by A after this period is
`P[1=(TR)/(100)]=Rs. 4000 [1+(10)/(200)]=Rs. 4000xx(21)/(20)=Rs. 4200`
Amount received by A after this period is `P[1+(R )/(100)]^(n)`
`R==(10%)/(4)=2.5%`
n=2 `(because " months " =2xx3` months)
`implies P[1+(R )/(100)]^(n)=Rs. 4000(1+(2.5)/(100))^(2)=Rs. 4000xx((41)/(40))^(2)=Rs. 4202.50`
`therefore` Profit of A= Rs. 4202.50-Rs. 4200=Rs. 2.50.