Question
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.Solution
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 months = 2 times because interest is calculated quarterly] ⇒ 6,120/75,000 = ( 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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