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Find the compounded interest on GH 10,000 at 12% rate for 10 months compound monthly

Mathematics

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Step-by-step solution

4 steps
  1. Identify the given values and the formula for compound interest.

    The principal amount (PP) is GH₵ 10,000.
    The annual interest rate (rr) is 12%, which is 0.12 in decimal form.
    The interest is compounded monthly, so the number of times interest is compounded per year (nn) is 12.
    The time period (tt) is 10 months, which is 1012\frac{10}{12} years.

    The formula for the total amount (AA) with compound interest is:

    A=P(1+rn)ntA = P\left(1 + \frac{r}{n}\right)^{nt}

    The compound interest (CICI) is then CI=A−PCI = A - P.

  2. Calculate the monthly interest rate and the total number of compounding periods.

    The monthly interest rate is rn=0.1212=0.01\frac{r}{n} = \frac{0.12}{12} = 0.01.
    The total number of compounding periods is nt=12×1012=10nt = 12 \times \frac{10}{12} = 10.

  3. Calculate the total amount (AA).

    Substitute the values into the formula:

    A=10000(1+0.01)10A = 10000\left(1 + 0.01\right)^{10} A=10000(1.01)10A = 10000(1.01)^{10} A=10000×1.10462212541A = 10000 \times 1.10462212541 A≈11046.22A \approx 11046.22
  4. Calculate the compound interest (CICI).

    Subtract the principal from the total amount:

    CI=A−PCI = A - P CI=11046.22−10000CI = 11046.22 - 10000 CI=1046.22CI = 1046.22

    The compound interest is GH₵ 1046.22.

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