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  • Compound Interest Formula and Facts


    Let Principal = P , Rate = R % per annum and Time = n years.

    1. Annual Compound Interest Formula:
    \begin{aligned}
    Amount = P\left( 1 + \frac{R}{100} \right)^n \\
    \end{aligned}

    2. Half Yearly Compound Interest Formula:
    When interest is compounded half yearly, then

    \begin{aligned}
    Amount = P\left( 1 + \frac{\frac{R}{2}}{100} \right)^{2n} \\
    \end{aligned}

    3. Quarterly Compound Interest Formula:
    When interest is compounded Quarterly, then
    \begin{aligned}
    Amount = P\left( 1 + \frac{\frac{R}{4}}{100} \right)^{4n} \\
    \end{aligned}

    4. When interest is compounded Annually but time is in fraction, say \begin{aligned}5\frac{2}{7} years \end{aligned}

    then Amount will be,

    \begin{aligned}
    Amount = P\left( 1 + \frac{R}{100} \right)^5 \times \left( 1 + \frac{\frac{2}{7}R}{100} \right)
    \end{aligned}

    5. When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year respectively.

    Then Amount will be,
    \begin{aligned}
    Amount = P\left( 1+\frac{R1}{100} \right) \left( 1+\frac{R2}{100} \right) \left( 1+\frac{R3}{100} \right)
    \end{aligned}

    6. Present worth of Rs. x due n years hence will be:

    \begin{aligned}
    \text{Present Worth} = \frac{x}{\left(1+\frac{R}{100}\right)^n}
    \end{aligned}