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Calculate the annual interest rate given the principal amount, simple interest earned, and time period.

Mathematics

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Answer

4.17%4.17\%

Step-by-step solution

6 steps
  1. Identify the given values.

    The principal amount is P=N20,000P = \text{N}20,000.
    The simple interest earned is I=N2,500I = \text{N}2,500.
    The time period is T=3T = 3 years.

  2. Use the simple interest formula.

    The formula for simple interest is:

    I=P×R×TI = P \times R \times T

    where II is the interest, PP is the principal, RR is the annual interest rate (as a decimal), and TT is the time in years.

  3. Rearrange the formula to solve for the interest rate RR.

    R=IP×TR = \frac{I}{P \times T}
  4. Substitute the given values into the formula.

    R=N2,500N20,000×3R = \frac{\text{N}2,500}{\text{N}20,000 \times 3}
  5. Calculate the interest rate.

    R=2,50060,000R = \frac{2,500}{60,000} R=25600R = \frac{25}{600} R=124R = \frac{1}{24} R≈0.041666...R \approx 0.041666...
  6. Convert the decimal rate to a percentage.

    To express the rate as a percentage, multiply by 100.

    R=0.041666...×100%R = 0.041666... \times 100\% R≈4.17%R \approx 4.17\%

    The interest rate is approximately 4.17%.

    4.17%\boxed{4.17\%}
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