Question

If the compound interest on a sum for 2 years at 12 (1/2)% per annum is Rs. 510, the simple interest on the same sum at the same rate for the same period of time is

A. Rs. 400 

B. Rs. 450 

C. Rs. 460 

D. Rs. 480

Answer 1

Compound interest, CI = Rs.510

Interest rate, R = \(12\frac{1}{2}\%\) = 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