If the compound interest on a sum for 2 years at 12% per annum is Rs. 510, the simple interest on the same sum at the same rate for the same period of time is

Compound interest, CI = Rs.510


Interest rate, R = 12% = 25/2% per annum


Time = 2 years


CI = P (1 + R/100)n – P


⇒ 510 = P (1 + (25/2)/100)2 – P


⇒ 510 = P (1 + 1/8)2 – P


⇒ 510 = P (9/8)2 – P


⇒ 510 = 81P/64 – P


⇒ 510 = (81P – 64P)/64


⇒ 510 = 17P/64


⇒ P = 510 × 64/17


⇒ P = 30 × 64


⇒ P = 1920


Now,


SI = PRT/100


= (1920 × 25/2 × 2)/100


= (1920 × 25)/100


= 480


∴ Simple interest = Rs.480

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