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Find the rate percent per annum simple interest for K420 to be the interest on K1200 invested for 5 years.

Mathematics

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Here are the solutions for questions 3, 4, 5, and 6.

3. Find the rate percent per annum simple interest for K420 to be the interest on K1200 invested for 5 years.

  1. Identify the given values for simple interest.

    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, and TT is the time in years.
    Given:
    Interest (II) = K420
    Principal (PP) = K1200
    Time (TT) = 5 years

  2. Rearrange the formula to solve for the rate (RR).

    R=IP×TR = \frac{I}{P \times T}
  3. Substitute the values and calculate the rate.

    R=K420K1200×5R = \frac{\text{K}420}{\text{K}1200 \times 5} R=4206000R = \frac{420}{6000} R=0.07R = 0.07
  4. Convert the decimal rate to a percentage.

    R=0.07×100%=7%R = 0.07 \times 100\% = 7\% 7% per annum\boxed{7\% \text{ per annum}}

    Refer to the given information to answer Questions 4 and 5
    K8 000 is invested for 12 years at 12% pa. The interest is compounded half-yearly.

    4. Calculate the amount after 12 years.

  5. Identify the given values for compound interest.

    The formula for compound amount is A=P(1+Rn)ntA = P \left(1 + \frac{R}{n}\right)^{nt}, where AA is the amount, PP is the principal, RR is the annual interest rate, nn is the number of times interest is compounded per year, and tt is the time in years.
    Given:
    Principal (PP) = K8 000
    Annual interest rate (RR) = 12% = 0.12
    Time (tt) = 12 years
    Compounding frequency (nn) = 2 (half-yearly)

  6. Calculate the values for Rn\frac{R}{n} and ntnt.

    Rn=0.122=0.06\frac{R}{n} = \frac{0.12}{2} = 0.06 nt=2×12=24nt = 2 \times 12 = 24
  7. Substitute the values into the compound amount formula and calculate.

    A=K8000(1+0.06)24A = \text{K}8000 \left(1 + 0.06\right)^{24} A=K8000(1.06)24A = \text{K}8000 \left(1.06\right)^{24} A=K8000×4.048905A = \text{K}8000 \times 4.048905 A=K32391.24A = \text{K}32391.24 K32391.24\boxed{\text{K}32391.24}

    5. Calculate the interest earned after 12 years.

  8. Use the amount calculated in Question 4 and the original principal.

    Amount (AA) = K32391.24
    Principal (PP) = K8 000

  9. Subtract the principal from the amount to find the interest earned.

    Interest Earned=A−P\text{Interest Earned} = A - P Interest Earned=K32391.24−K8000\text{Interest Earned} = \text{K}32391.24 - \text{K}8000 Interest Earned=K24391.24\text{Interest Earned} = \text{K}24391.24 K24391.24\boxed{\text{K}24391.24}

    6. Evaluate: K5 000 (1+17%)5=(1 + 17\%)^5 =

  10. Convert the percentage to a decimal and add it to 1.

    1+17%=1+0.17=1.171 + 17\% = 1 + 0.17 = 1.17
  11. Raise the result to the power of 5.

    (1.17)5≈2.19245(1.17)^5 \approx 2.19245
  12. Multiply the result by K5 000.

    K5000×2.19245\text{K}5000 \times 2.19245 K10962.25\text{K}10962.25 K10962.25\boxed{\text{K}10962.25}
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