Multiple choice

There are two schemes. Scheme 1: Simple interest at 50% per annum for one and half years. Scheme 2: Compound interest compounded half-yearly at 50% per annum for one and half years. Which scheme is better and approximately by how much percent?

  1. Scheme 2 is better by 15% percent

  2. Scheme 1 is better by 15% percent

  3. Scheme 1 is better by 20% percent

  4. Scheme 2 is better by 20% percent

  5. Both schemes give same amount
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Scheme 1: SI = 50% * 1.5 = 75%. Scheme 2: CI at 25% per half-year for 3 periods. Amount = P(1 + 0.25)^3 = P(1.25)^3 = P(1.953125). Interest = 95.3125%. Difference = 95.31 - 75 = 20.31%. Approximately 20%.

AI explanation

Assuming a principal of 100, Scheme 1 yields a final amount of 175 using the simple interest formula, where 100 plus 100 multiplied by 0.5 multiplied by 1.5 equals 175. Scheme 2 compounds semi-annually, so the amount is 100 multiplied by 1.25 raised to the power of three, resulting in 195.3125. The percentage difference between the two schemes is calculated from their base interest amounts, making Scheme 2 better than Scheme 1 by 20 percent.

Keep practicing — related questions