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Calculate the rate of interest for the following principal, interest, and time periods: a) P=4000, I=800, T=2yrs b) P=3000, I=1350, T=3yrs c) P=10000, I=4000, T=4yrs

Mathematics

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To find the rate of interest, we use the simple interest formula:

I=P⋅R⋅TI = P \cdot R \cdot T

Where II is the Interest, PP is the Principal, RR is the Rate of interest (as a decimal), and TT is the Time in years.
We can rearrange this formula to solve for RR:

R=IP⋅TR = \frac{I}{P \cdot T}

Part a· 3 steps

  1. Identify the given values.

    P=Rs 4000P = \text{Rs } 4000
    I=Rs 800I = \text{Rs } 800
    T=2 yrsT = 2 \text{ yrs}

  2. Substitute the values into the formula for RR.

    R=8004000×2R = \frac{800}{4000 \times 2} R=8008000R = \frac{800}{8000} R=0.1R = 0.1
  3. Convert the decimal rate to a percentage.

    R=0.1×100%=10%R = 0.1 \times 100\% = 10\%

    The rate of interest is 10%\boxed{\text{10\%}}.

Part b· 3 steps

  1. Identify the given values.

    P=Rs 3000P = \text{Rs } 3000
    I=Rs 1350I = \text{Rs } 1350
    T=3 yrsT = 3 \text{ yrs}

  2. Substitute the values into the formula for RR.

    R=13503000×3R = \frac{1350}{3000 \times 3} R=13509000R = \frac{1350}{9000} R=0.15R = 0.15
  3. Convert the decimal rate to a percentage.

    R=0.15×100%=15%R = 0.15 \times 100\% = 15\%

    The rate of interest is 15%\boxed{\text{15\%}}.

Part c· 3 steps

  1. Identify the given values.

    P=Rs 10000P = \text{Rs } 10000
    I=Rs 4000I = \text{Rs } 4000
    T=4 yrsT = 4 \text{ yrs}

  2. Substitute the values into the formula for RR.

    R=400010000×4R = \frac{4000}{10000 \times 4} R=400040000R = \frac{4000}{40000} R=0.1R = 0.1
  3. Convert the decimal rate to a percentage.

    R=0.1×100%=10%R = 0.1 \times 100\% = 10\%

    The rate of interest is 10%\boxed{\text{10\%}}.

Part d· 3 steps

  1. Identify the given values.

    P=Rs 15000P = \text{Rs } 15000
    I=Rs 7500I = \text{Rs } 7500
    T=5 yrsT = 5 \text{ yrs}

  2. Substitute the values into the formula for RR.

    R=750015000×5R = \frac{7500}{15000 \times 5} R=750075000R = \frac{7500}{75000} R=0.1R = 0.1
  3. Convert the decimal rate to a percentage.

    R=0.1×100%=10%R = 0.1 \times 100\% = 10\%

    The rate of interest is 10%\boxed{\text{10\%}}.

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