Multiple choice

On a certain sum of money lent out at 16% p.a. the difference between the compound interest for 1 year, payable half yearly, and the simple interest for 1 year is Rs. 56. The sum is

  1. Rs. 1,080

  2. Rs. 7,805

  3. Rs. 8,750

  4. Rs. 5,780

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simple Interest (SI) = P * 0.16 * 1 = 0.16P. Compound Interest (CI) half-yearly at 16% p.a. means 8% per half-year for 2 periods: CI = P * (1.08^2 - 1) = P * (1.1664 - 1) = 0.1664P. Difference = 0.1664P - 0.16P = 0.0064P = 56. P = 56 / 0.0064 = 8750.

AI explanation

Using the effective rate formula, the compound interest rate for 1 year payable half yearly is calculated as 8 plus 8 plus 0.64, which equals 16.64 percent. The difference between this compound interest and the simple interest at 16 percent is 0.64 percent of the principal. Since this difference is Rs. 56, the principal equals 56 divided by 0.0064, which gives the sum as Rs. 8750.

Keep practicing — related questions