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 per cent per annum, CI = P [(1 + (R/100))ᵀ - 1] ⇒ 6,120 = 75,000 [(1 + (R/400))2 - 1 ] [T = 6× 4 = 24 months = 2 yrs because interest is calculated quarterly] ⇒ 6120/75000 = (1 + (R/400)) 2 - 1 ⇒ (1 + (R/400))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× R× T)/100) = (75000× 16× 18)/(100× 12) = 18,000
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