Quarterly Compounding Calculations
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Questions and Answers

What is the formula used for calculating the amount after quarterly compounding?

  • $f_1 = (1 + i)^4$
  • $f_1 = (1 + rac{i}{12})^{12}$
  • $f_1 = (1 + rac{i}{4})^4$ (correct)
  • $f_1 = (1 + rac{i}{2})^2$

    • If a principal is compounded quarterly at 6% for three years, what value does it approach?

  • 1.030225 (correct)
  • 1.15536
  • 1.06045
  • 1.030243

    • What is the nominal rate compounded semiannually that will result in an equivalent amount as quarterly compounding at 6%?

  • 4.5%
  • 5%
  • 3% (correct)
  • 6.05%

    • Which step involves taking the square root in the calculation of the equivalent semiannual nominal rate?

    <p>Solving $1.030225 = rac{(1+r/2)^2}$ (A)</p> Signup and view all the answers

    To reach the same compound amount after three years of quarterly compounding, how is the effective rate calculated from the nominal rate?

    <p>$r = 2 imes r_{nominal}$ (B)</p> Signup and view all the answers

    What value does $r$ equal when solving for the nominal rate in the semiannual compounding formula?

    <p>0.03 (A)</p> Signup and view all the answers

    What is the approximate effective annual rate derived from a nominal rate of 3% compounded semiannually?

    <p>6.05% (A)</p> Signup and view all the answers

    Flashcards

    What is principal?

    The initial amount of money invested or borrowed.

    What is the interest rate?

    The rate at which interest is calculated and added to the principal over a specific period, expressed as a percentage.

    What is compounding frequency?

    The number of times interest is compounded within a year. For example, quarterly compounding means interest is calculated four times a year.

    What is compound amount?

    The total amount accumulated after a certain period, including both the original principal and the accrued interest.

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    What is effective annual rate?

    The rate expressed as a percentage that represents the annual growth of an investment after taking into account the effects of compounding.

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    What is the formula for compound amount?

    The formula used to calculate the compound amount ("S") when interest is compounded at a certain frequency.

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    What is the purpose of this problem?

    Finding the nominal rate that yields the same compound amount for different compounding frequencies.

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