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Calculate the time in years for an investment of N15,000 at a 5% simple annual interest rate to yield N4,500 in interest.

Mathematics

ScanSolve AI Answer

Answer

6 years6 \text{ years}

Step-by-step solution

6 steps

  1. Identify the given values for question 4.

    The principal amount is P=N15,000P = \text{N}15,000.
    The annual interest rate is R=5%R = 5\%.
    The simple interest to be yielded is I=N4,500I = \text{N}4,500.

  2. Convert the interest rate from a percentage to a decimal.

    R=5%=5100=0.05R = 5\% = \frac{5}{100} = 0.05

  3. Use the simple interest formula and rearrange it to solve for time TT.

    The formula for simple interest is:

    I=P×R×TI = P \times R \times T

    To find the time TT, rearrange the formula:

    T=IP×RT = \frac{I}{P \times R}

  4. Substitute the given values into the formula.

    T=N4,500N15,000×0.05T = \frac{\text{N}4,500}{\text{N}15,000 \times 0.05}

  5. Calculate the denominator.

    15,000×0.05=75015,000 \times 0.05 = 750

  6. Calculate the time TT.

    T=4,500750T = \frac{4,500}{750} T=6T = 6

    The time taken is 6 years.

    6 years6 \text{ years}
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