If the simple interest on a certain sum for 1.5 years at 8% p.a is Rs 360.…

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If the simple interest on a certain sum for 1.5 years at 8% p.a is Rs 360. Find the compound interest on the same sum for the same rate of interest but double the time ?

  1. A.

    Rs 778

  2. B.

    Rs 778.13

  3. C.

    Rs 779.13

  4. D.

    Rs 777.13

Attempted by 8 students.

Show answer & explanation

Correct answer: C

Step-by-Step Solution

To find the compound interest, we first need to determine the principal amount using the simple interest information provided.

  1. Calculate the Principal (P):

    • Formula: SI = (P * r * t) / 100

    • Given: SI = 360, r = 8%, t = 1.5 years

    • 360 = (P * 8 * 1.5) / 100

    • 360 = (P * 12) / 100

    • 360 * 100 = 12 * P

    • 36,000 = 12 * P

    • P = 3,000

  2. Calculate Compound Interest (CI):

    • Time is doubled: t = 1.5 years * 2 = 3 years.

    • Rate: r = 8%

    • Formula for Amount (A) with CI: A = P * (1 + r/100)^t

    • A = 3000 * (1 + 8/100)^3

    • A = 3000 * (1.08)^3

    • A = 3000 * 1.259712

    • A = 3,779.136

  3. Find the Interest:

    • CI = Amount - Principal

    • CI = 3,779.136 - 3,000

    • CI = 779.136 (approximately Rs. 779.13)

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