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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 (B)

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. (A)</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. (D)</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 (B)</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 (A)</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 (D)</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 (A)</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 (A)</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 (A)</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 (D)</p> Signup and view all the answers

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

<p>False (B)</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 (C)</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 (B)</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 (A)</p> Signup and view all the answers

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

<p>False (B)</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 (C)</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 (C)</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 (A)</p> Signup and view all the answers

A cash inflow can be represented by a positive number.

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

Deferred annuities represent regular payments made beginning immediately.

<p>False (B)</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 (C)</p> Signup and view all the answers

Flashcards

Simple Annuity

Payments and interest compounding happen at the same intervals (e.g., both monthly).

General Annuity

Payment intervals don't match interest compounding periods (e.g., monthly payments, but semi-annual interest).

Annuity Certain

An annuity with a fixed starting and ending date.

Perpetuity

An annuity with a fixed starting date but never ends (principal remains intact).

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Contingent Annuity

An annuity with a fixed starting date but an uncertain ending date that depends on events.

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Ordinary Annuity

Payments are made at the end of each interval.

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Annuity Due

Payments are made at the beginning of each interval.

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Deferred Annuity

Payments are made at a later time, not at the beginning or end of the interval.

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Future Value of an Ordinary Annuity (F)

The total amount accumulated at the end of the annuity period.

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R

The fixed amount of each payment made in the ordinary annuity.

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i

The interest rate per compounding period.

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n

The total number of payments in the annuity (number of compounding periods).

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r

The nominal interest rate per year.

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m

The number of compounding periods in a year, usually matching the payment frequency.

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t

The total time period of the annuity.

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Cash Flow

The movement of money into (inflows) or out of (outflows) a business or individual's account.

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Present Value (PV) of Deferred Annuity

The current value of the future payments that make up a deferred annuity.

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Future Value (FV) of Deferred Annuity

The total amount accumulated at the end of a deferred annuity.

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P (Regular Payment)

The fixed amount of each payment made in the deferred annuity.

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i (Interest Rate per Conversion Period)

Rate of interest that applies per compounding period.

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n (Number of Paying Periods)

The total number of payments made during the annuity period.

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d (Number of Deferred Periods)

The number of periods before the annuity starts making payments.

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Converting Annual Interest Rate

The process of changing an annual interest rate to a rate per compounding period.

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Calculating Number of Paying Periods

Multiplying the number of years by the number of compounding periods per year.

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What is a General Annuity?

In a general annuity, payment intervals and interest compounding periods don't match. For example, monthly payments with annual interest compounding.

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What is a General Ordinary Annuity?

A general annuity where payments are made at the end of each payment interval.

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Interest Rate (i) for General Annuities

The interest rate per payment period. Calculated as (1 + r/ m2) ^ (m2/m1) - 1, where 'r' is the annual interest rate, 'm1' is the frequency of payments, and 'm2' is the frequency of compounding.

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Future Value (F) of a General Annuity

The total amount accumulated at the end of the annuity period. Calculated as: F = R[(1 + i)^n -1] /i, where 'R' is the payment amount, 'i' is the interest rate per period, and 'n' is the number of payments.

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Example: Monthly Payments, Annual Compounding

A car loan with monthly payments but an annual interest rate is a General Annuity. The interest is calculated only once a year, but payments are made monthly, making the payment and compounding periods different.

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Example: Semi-annual Payments, Monthly Compounding

Paying a debt bi-annually (twice a year) while the bank calculates interest monthly is a General Annuity. This indicates different payment and compounding intervals.

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Frequency of Payments ('m1')

Number of payments per year. For example, monthly payments have 'm1' = 12, while annual payments have 'm1' = 1.

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Frequency of Compounding ('m2')

Number of times interest is compounded per year. For example, monthly compounding has 'm2' = 12, while semi-annual compounding has 'm2' = 2.

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Cash Equivalent of a Lot

The total present value of all payments made for a property, including the down payment and future installment payments.

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Amount of an Annuity

The future value of an annuity that represents the total amount accumulated at the end of the annuity period, considering all the payments and interest earned.

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Present Value of an Annuity

The current value of the future payments of an annuity, considering the time value of money, meaning a future payment is worth less today.

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What is the 'd' in the Annuity Formula?

'd' represents the number of payment periods that the annuity is deferred.

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How to calculate 'n' in Annuity Formulas?

'n' is the total number of payment periods in the annuity, calculated by multiplying the number of years by the number of payments per year.

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What is 'i' in Annuity Formulas?

'i' represents the interest rate per compounding period, calculated by dividing the annual interest rate by the number of compounding periods per year.

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Why is the formula for present value of deferred annuity?

The formula accounts for the two phases of the annuity: (1) the delay period before payments begin, and (2) the period of regular payments.

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What is 'K' in the Annuity Formula?

'K' represents the number of interest compounding periods per year.

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Key Factor in Annuities:

The present value (PV) of an annuity represents the lump sum amount needed today to finance a series of future payments.

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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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