Annuities and Their Types

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.

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.