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Questions and Answers

What is a simple annuity?

  • Payments can occur at any time without regular intervals.
  • Payments coincide with interest compounding periods. (correct)
  • Payments are made at the end of each period regardless of interest.
  • It has an indefinite term and earns interest continuously.

    • A perpetuity has a fixed end date.

    False

    Define contingent annuity.

    An annuity that begins on a definite date but ends based on uncertain future conditions.

    In an ordinary annuity, payments are made at the ______ of each payment interval.

    <p>end</p> Signup and view all the answers

    Which of the following correctly describes a deferred annuity?

    <p>Payments do not start until a specified future date.</p> Signup and view all the answers

    Match the following annuities with their characteristics:

    <p>Simple Annuity = Coincides with interest compounding periods General Annuity = Does not coincide with interest compounding periods Annuity Due = Payments at the beginning of each period Ordinary Annuity = Payments at the end of each period</p> Signup and view all the answers

    How is interest calculated in a general annuity?

    <p>Based on a different frequency than the payment interval.</p> Signup and view all the answers

    What is an annuity certain?

    <p>An annuity that has a fixed start and end date.</p> Signup and view all the answers

    Which type of annuity has payments made at the beginning of each payment interval?

    <p>Annuity Due</p> Signup and view all the answers

    The present value of an annuity is the total of all future payments discounted to their present worth.

    <p>True</p> Signup and view all the answers

    What is the term used to describe the sum of future values of all payments in an annuity?

    <p>Future Value</p> Signup and view all the answers

    An annuity where the payments have specified start and end times is called an ______.

    <p>Annuity Certain</p> Signup and view all the answers

    Match the following terms with their definitions:

    <p>Annual Payment = Payment made each year Present Value = Current worth of future payments Future Value = Value of payments at a future date Periodic Payment = Regular intervals of payment</p> Signup and view all the answers

    What does the formula for the future value of an ordinary annuity (F) primarily depend on?

    <p>All of the above</p> Signup and view all the answers

    In the formula for ordinary annuities, 'm' refers to the number of payments made in a year.

    <p>True</p> Signup and view all the answers

    What is the formula to calculate the interest rate per period in an ordinary annuity?

    <p>i = r/m</p> Signup and view all the answers

    In the context of an ordinary annuity, the term 'F' stands for the ________ value.

    <p>future</p> Signup and view all the answers

    Which part of the ordinary annuity formula signifies the number of periods?

    <p>n</p> Signup and view all the answers

    Define the term 'ordinary annuity'.

    <p>An ordinary annuity is a series of equal payments made at the end of each period.</p> Signup and view all the answers

    Match the components of the ordinary annuity formula with their meanings:

    <p>F = Future value R = Equal payment i = Interest rate per period n = Number of periods</p> Signup and view all the answers

    The expression 'n = mt' indicates that the total number of periods is the product of the payment intervals and the term of the investment.

    <p>True</p> Signup and view all the answers

    What is the present value of 10 semi-annual payments of ₱2,000 at an interest rate of 8% compounded semi-annually?

    <p>₱13,333.13</p> Signup and view all the answers

    A deferred annuity pays its installments at the end of each payment period.

    <p>False</p> Signup and view all the answers

    What is the interest rate 'i' used when calculating the present value for a 6% annual interest rate compounded quarterly?

    <p>0.015</p> Signup and view all the answers

    The present value of an annuity includes payments made at equal intervals and is affected by the ___________.

    <p>interest rate</p> Signup and view all the answers

    If an annuity pays ₱1,500 for 8 years at an interest rate of 6%, what is its present value?

    <p>₱31,699.68</p> Signup and view all the answers

    The formula used for calculating the present value of an annuity is the same regardless of the payment frequency.

    <p>False</p> Signup and view all the answers

    What is the total number of payments (n) in the annuity that pays ₱5,000 per quarter for 10 years?

    <p>40</p> Signup and view all the answers

    What is the future value of Mrs. Remoto's savings after 6 months if she saves 3,000 pesos monthly at an interest rate of 9% compounded monthly?

    <p>18,832.25 pesos</p> Signup and view all the answers

    In a general annuity, the payment intervals are always the same as the compounding intervals.

    <p>False</p> Signup and view all the answers

    What does the variable 'R' represent in annuity formulas?

    <p>The periodic payment amount.</p> Signup and view all the answers

    In Marie's savings plan, she saves 200 pesos at the end of each month for ____ years.

    <p>6</p> Signup and view all the answers

    What is the value of 'i' if the monthly interest rate 'r' is 0.0025?

    <p>0.0075</p> Signup and view all the answers

    Match the following individuals with their respective savings amount per month:

    <p>Mrs. Remoto = 3,000 pesos Marie = 200 pesos Alex = 2,000 pesos</p> Signup and view all the answers

    How long does Alex invest in his savings account?

    <p>6 years</p> Signup and view all the answers

    The future value of an annuity involves calculating the payments made for a period of ____ years.

    <p>9</p> Signup and view all the answers

    How much money will Marie have at the end of her 6-year savings plan if the bank pays 0.25% compounded monthly?

    <p>15,986.57 pesos</p> Signup and view all the answers

    What is the value of the future cash flow (F) calculated from the given data?

    <p>$53,318.83 pesos</p> Signup and view all the answers

    A cash inflow can be represented by a positive number.

    <p>True</p> Signup and view all the answers

    How is the rate per conversion period (i) calculated?

    <p>i = r/K</p> Signup and view all the answers

    The number of periods in a deferred annuity can be calculated using the formula n = ____ × K.

    <p>t</p> Signup and view all the answers

    What is the annual interest rate (r) given in the data?

    <p>0.06</p> Signup and view all the answers

    Deferred annuities represent regular payments made beginning immediately.

    <p>False</p> Signup and view all the answers

    What is the value of n calculated using m1 and t?

    <p>24</p> Signup and view all the answers

    The number of deferred periods is represented by ____ in the formula.

    <p>d</p> Signup and view all the answers

    Which formula correctly represents the future value (FV) of a deferred annuity?

    <p>FV = P[ (1 + i)^{n} - 1 ] / i</p> Signup and view all the answers

    Study Notes

    Introduction to Annuities

    • Annuities are contracts promising regular income, either immediately or later.
    • They can be purchased with a lump sum or periodic payments.
    • Payments are made at equal intervals (annually, semi-annually, etc.).
    • The sum of compounded amounts is the annuity amount.
    • The time between payments is the payment interval.
    • The time from the start to the last payment is the term of the annuity.

    Objectives

    • Learners will understand simple and general annuities.
    • Learners will differentiate between simple and general annuities.
    • Learners will calculate future and present values of simple annuities.

    Classification of Annuities

    • By Length of Payment Intervals and Interest Compounding Period:
      • Simple Annuity: Payment interval matches interest compounding period (e.g., semi-annual payments with semi-annual compounding). Interest is calculated on the payment date.
      • General Annuity: Payment interval doesn't match interest compounding period (e.g., monthly payments with annual compounding). Interest is calculated at different times.
    • By Term:
      • Annuity Certain: Starts and ends on definite dates (e.g., a loan).
      • Perpetuity: Starts on a definite date but never ends (principal remains and earns interest).
      • Contingent Annuity: Start date is definite, but the end date depends on a future event.

    Ordinary Annuity

    • Payments are made at the end of each period.
    • The amount of an ordinary annuity is the sum of periodic payments at the end of the term.

    General Annuity

    • The interest compounding period does not match the payment interval.

    Deferred Annuity

    • An annuity that begins after a specified period (deferral period).
    • The present and future value formulas account for the deferral period.

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