Annuities and Their Types

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Questions and Answers

What is the formula used to calculate the future value of an ordinary annuity?

$FV_{OA} = A \cdot \frac{(1+p)^{-n}}{p}$

$FV_{OA} = A \cdot (1+i)^n$

$FV_{OA} = A \cdot (1+p)^{-n}$

$FV_{OA} = A \cdot \frac{(1+i)^n - 1}{i}$ (correct)

When payments are made at the beginning of each period, what is this type of annuity called?

Present Annuity

Future Annuity

Annuity Due (correct)

Ordinary Annuity

How do you calculate the present value of an ordinary annuity?

$PV_{OA} = A \cdot \frac{1-(1+i)^{-n}}{i}$ (correct)

$PV_{OA} = A \cdot (1+i)^{-n}$

$PV_{OA} = A \cdot \frac{1+(1+i)^{-n}}{i}$

$PV_{OA} = A \cdot \frac{(1+i)^{n}-1}{i}$

In the future value formula for a general annuity, what does 'p' represent?

Periodic interest rate Signup and view all the answers

What is the main difference between ordinary annuity and annuity due?

Timing of payments Signup and view all the answers

What is the future value of a series of payments of Php 918 made at the end of every quarter for 4 years at an interest rate of 4.8% compounded annually?

Php 49,312.62 Signup and view all the answers

What is the present value of a series of payments of Php 850 made at the beginning of every month for 2 years at an interest rate of 6% compounded semi-annually?

Php 16,403.25 Signup and view all the answers

If the interest rate is compounded quarterly, how would you express the periodic interest rate for an annual rate of 4.8%?

0.012 Signup and view all the answers

What is the correct approach to calculate the future value if the payment is made at the beginning of each period?

Apply the future value of ordinary annuity formula and adjust by multiplying with (1+i) Signup and view all the answers

If a payment of Php 1,950 is made at the end of every quarter for 4 years at an annual interest rate of 6% compounded monthly, what is the future value?

Php 38,037.80 Signup and view all the answers

When calculating the present value of a general annuity, what does 'm' represent?

The number of compounding periods in which payments are made Signup and view all the answers

Calculate the future value of a deposit of Php 1,020 made at the beginning of each month for 4 years with an annual interest rate of 7.2% compounded annually.

Php 54,234.45 Signup and view all the answers

What effect does compounding frequently have on the future value of an annuity?

Increases the total future value Signup and view all the answers

What is the present value of a series of payments of Php 2,500 made at the end of every 6 months for 10 years at an annual interest rate of 6% compounded semi-annually?

Php 22,960.37 Signup and view all the answers

What is the primary factor that influences both the future and present value of an annuity?

Interest rate Signup and view all the answers

What is the primary feature of an ordinary annuity?

Payments are made at the end of each period. Signup and view all the answers

In the formula for future value of an ordinary annuity, what does 'A' represent?

The equal payment amount per period. Signup and view all the answers

What does the variable 'n' stand for in the annuity formulas?

Number of compounding periods. Signup and view all the answers

Which formula calculates the present value of an ordinary annuity?

$PV_{OA} = A rac{1 - (1 + i)^{-n}}{i}$ Signup and view all the answers

In a general annuity, what is the primary distinction from an ordinary annuity?

Payments vary from period to period. Signup and view all the answers

Which formula correctly represents the future value of an annuity due?

$FV_{AD} = A (1 + i) rac{(1 + i)^{n} - 1}{i}$ Signup and view all the answers

What is the effect of increasing the interest rate (i) on the future value of an ordinary annuity?

It increases the future value of the annuity. Signup and view all the answers

Which variable represents the periodic interest rate in annuity calculations?

i Signup and view all the answers

When might an annuity due be more beneficial than an ordinary annuity?

When cash flow is received earlier. Signup and view all the answers

In which context would you use an ordinary annuity formula?

For a loan amortized with monthly payments. Signup and view all the answers

What is a simple annuity?

An annuity where the payment interval coincides with the interest period. Signup and view all the answers

What type of annuity is used when payments are made at the end of each period?

Ordinary Annuity Signup and view all the answers

Which of the following describes an annuity due?

Payments are made at the beginning of each payment interval. Signup and view all the answers

In which scenario does a general annuity typically occur?

Payments occur at varying periods based on a schedule. Signup and view all the answers

When is a contingent annuity applicable?

When payments depend on random life events or conditions. Signup and view all the answers

Which type of annuity would best describe Rene's car installment payment plan?

Simple Annuity Signup and view all the answers

How is the payment interval defined in a simple annuity?

It equals the interest period. Signup and view all the answers

Identify the correct definition of an ordinary annuity.

Payments made at the end of each period. Signup and view all the answers

Study Notes

Future Value of an Ordinary Annuity

The formula to calculate the future value (FV) of an ordinary annuity is: FV = A * (((1 + i)^n - 1) / i)
'A' represents the amount of each payment
'i' represents the periodic interest rate
'n' represents the total number of payment periods

Annuity Due

An annuity due is a type of annuity where payments are made at the beginning of each period, rather than at the end.

Present Value of an Ordinary Annuity

The formula to calculate the present value (PV) of an ordinary annuity is: PV = A * ((1 - (1 + i)^-n) / i)

General Annuity

In the future value formula for a general annuity, 'p' represents the number of compounding periods per year.

Difference Between Ordinary Annuity and Annuity Due

The main difference between an ordinary annuity and an annuity due is the timing of payments. In an ordinary annuity, payments are made at the end of each period, while in an annuity due, payments are made at the beginning of each period.

Calculating Future Value

To calculate the future value of a series of payments made at the end of every quarter for 4 years at an interest rate of 4.8% compounded annually, you would need to use the future value formula for an ordinary annuity.

Present Value

To calculate the present value of a series of payments made at the beginning of every month for 2 years at an interest rate of 6% compounded semi-annually, you would need to use the present value formula for an annuity due.

Periodic Interest Rate

If the interest rate is compounded quarterly, the periodic interest rate for an annual rate of 4.8% would be 4.8%/4 = 1.2% per quarter.

Future Value with Payments at the Beginning

To calculate the future value when payments are made at the beginning of each period, you would need to use the future value formula for an annuity due.

Future Value Calculation

The future value of a payment of Php 1,950 made at the end of every quarter for 4 years at an annual interest rate of 6% compounded monthly is calculated using the future value formula for an ordinary annuity.

Present Value of a General Annuity

In the present value formula for a general annuity, 'm' represents the number of payment periods per year.

Future Value of a Deposit

The future value of a deposit of Php 1,020 made at the beginning of each month for 4 years with an annual interest rate of 7.2% compounded annually is calculated using the future value formula for an annuity due.

Effect of Compounding Frequency

Compounding more frequently (e.g., quarterly instead of annually) generally leads to a higher future value of an annuity, as interest is earned on interest more often.

Present Value of a Series of Payments

The present value of a series of payments of Php 2,500 made at the end of every 6 months for 10 years at an annual interest rate of 6% compounded semi-annually is calculated using the present value formula for an ordinary annuity.

The Primary Factor

The primary factor that influences both the future and present value of an annuity is the interest rate (i).

Primary Feature of an Ordinary Annuity

The primary feature of an ordinary annuity is that payments are made at the end of each period.

'A' in the Future Value Formula

In the formula for future value of an ordinary annuity, 'A' represents the amount of each payment.

'n' in Annuity Formulas

The variable 'n' in the annuity formulas stands for the total number of payment periods.

Formula for Present Value of an Ordinary Annuity

The formula that calculates the present value of an ordinary annuity is: PV = A * ((1 - (1 + i)^-n) / i)

Distinction in a General Annuity

The primary distinction between a general annuity and an ordinary annuity is that a general annuity allows for a different number of compounding periods per year than payment periods per year.

Future Value of an Annuity Due Formula

The formula that correctly represents the future value of an annuity due is: FV = A * (((1 + i)^n - 1) / i) * (1 + i)

Effect of Increasing the Interest Rate

Increasing the interest rate (i) will generally lead to a higher future value of an ordinary annuity.

Periodic Interest Rate Variable

The variable that represents the periodic interest rate in annuity calculations is 'i'.

When an Annuity Due is More Beneficial

An annuity due may be more beneficial than an ordinary annuity when you want to maximize the amount of interest earned, as payments are made earlier and earn interest for a longer period.

Using an Ordinary Annuity Formula

You would use an ordinary annuity formula when payments are made at the end of each period.

Simple Annuity

A simple annuity is a type of annuity where both the payment periods and compounding periods occur at the same frequency.

Type of Annuity Used

The type of annuity used when payments are made at the end of each period is an ordinary annuity.

Describing an Annuity Due

An annuity due is described as a type of annuity where payments are made at the beginning of each period.

When a General Annuity Occurs

A general annuity typically occurs when the compounding period is different from the payment period.

Contingent Annuity

A contingent annuity is applicable when the payment period is dependent upon the occurrence of a specific event.

Rene's Car Installment Plan

Rene's car installment payment plan would best be described as an ordinary annuity, as the payments are likely made at the end of each month.

Payment Interval in a Simple Annuity

The payment interval in a simple annuity is defined by the frequency of the payments.

Definition of an Ordinary Annuity

An ordinary annuity is defined as a series of equal payments made at the end of each period for a specified duration.

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Description

Explore the concept of annuities, including various types such as simple, ordinary, and contingent annuities. This quiz covers definitions, formulas for calculating future values, and distinctions between payment intervals. Test your understanding of these financial instruments.