At a certain rate per annum, the simple interest on a sum of money for one…

2024

At a certain rate per annum, the simple interest on a sum of money for one year is Rs. 260 and the compound interest on the same sum for two years is Rs. 540.80. The rate of interest per annum is = ?

  1. A.

    6%

  2. B.

    2%

  3. C.

    8%

  4. D.

    7%

Attempted by 1 students.

Show answer & explanation

Correct answer: C

Step-by-Step Solution

To find the rate of interest, we can utilize the relationship between the simple interest for one year and the compound interest for two years.

  1. Calculate the Simple Interest for 2 years:

    • SI for 1 year = Rs. 260.

    • Since SI is constant each year, SI for 2 years = 260 * 2 = Rs. 520.

  2. Determine the difference between CI and SI for 2 years:

    • CI for 2 years = Rs. 540.80.

    • SI for 2 years = Rs. 520.00.

    • Difference = 540.80 - 520 = Rs. 20.80.

  3. Understand the concept:

    • The difference between CI and SI for 2 years is essentially the interest earned on the interest of the first year.

    • In other words, the interest of Rs. 20.80 is earned on the first year's interest of Rs. 260.

  4. Calculate the rate (R):

    • R = (Difference / SI for 1 year) * 100

    • R = (20.80 / 260) * 100

    • R = 0.08 * 100 = 8%

Explore the full course: Amcat Preparation