A college student bought a new bike and he got insurance for it. He is paying…

2025

A college student bought a new bike and he got insurance for it. He is paying that money at simple interest, but he should include the interest for every six months for calculating the principal. If he undergoes a charge at an interest rate of 15%, the effective rate of interest becomes:

  1. A.

    15.56%

  2. B.

    23%

  3. C.

    20%

  4. D.

    21%

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Show answer & explanation

Correct answer: A

Step-by-Step Solution

To calculate the effective rate of interest when a 15% annual interest rate is compounded semi-annually (every six months), follow these steps:

  1. Adjust the annual rate for the semi-annual period:

    • Annual interest rate = 15%.

    • Since compounding occurs semi-annually, the interest rate per period is half of the annual rate.

    • Interest rate per period = 15% / 2 = 7.5%.

  2. Calculate the effective annual rate using the successive percentage increase formula:

    • The formula for two successive increases of 'a' and 'b' is: a + b + (a * b) / 100.

    • Here, both periods have a rate of 7.5%.

    • Effective Rate = 7.5 + 7.5 + (7.5 * 7.5) / 100

    • Effective Rate = 15 + 56.25 / 100

    • Effective Rate = 15 + 0.5625

    • Effective Rate = 15.56%.

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