At what rate percent per annum will Rs. 75,000 yields a compound interest of Rs. 6,120 in 6 months, if the interest is being compounded quarterly? Calculate the simple interest at the same rate of interest for 18 months.

Let the rate of C.I be R percent per annum, CI = P [ ( 1 + `(R)/(100)` )ᵀ - 1] ⇒ 6,120 = 75,000 [ ( 1 + `(R)/(400)` )² - 1 ] [T= 6 months = 2 because interest is calculated quarterly] ⇒ `(6120)/(75000)` = ( 1 +`(R)/(400)` ) ² - 1 ⇒ ( 1 + ) ² - 1 = `(51)/(625)` ` ` ⇒ ( 1 + `(R)/(400)` ) ² = 1 + `(51)/(625)` ⇒ ( 1 + `(R)/(400)` )² = `(676)/(625)` ⇒ ( 1 +`(R)/(400)` )² = ( `(26)/(25)` )² ⇒ 1+ `(R)/(400)` = `(26)/(25)` ⇒ `(R)/(400)` = `(26)/(25)` - 1 = `(1)/(25)` R = `(400)/(25)` = 16% Now, S.I = `(P xx R xx T)/(100)` = `(75000 xx 16 xx 18)/(100 xx 12)` = Rs. 18,000