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

Question

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

Philoid · Accepted Answer

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