Fundamental of AnnuitiesAn annuity is a continuous stream of equal periodic payments from one party to another for a specified period of time to fulfill a financial obligation. An annuity payment is the dollar amount of the equal periodic payment in an annuity environment. The payments are continuous, equal, periodic, and occur over a fixed time frame. If any one of these four characteristics is not satisfied, then the financial transaction fails to meet the definition of a singular annuity and requires other techniques and formulas to solve. Show
There are four types of annuities, which are based on the combination of two key characteristics: timing of payments and frequency. Four Types of AnnuitiesOrdinary Simple AnnuityAn ordinary simple annuity has the following characteristics:
Ordinary General AnnuityAn ordinary general annuity has the following characteristics:
Simple Annuity DueA simple annuity due has the following characteristics:
General Annuity DueA general annuity due has the following characteristics:
The table below summarizes the four types of annuities and their characteristics for easy reference. Table 11.1.1. Four Types of Annuities and Their Characteristics
One of the most challenging aspects of annuities is recognizing whether the annuity you are working with is ordinary or due. This distinction plays a critical role in formula selection later in this chapter. To help you recognize the difference, the table below summarizes some key words along with common applications in which the annuity may appear. Table 11.1.2. Ordinary Versus Due Annuities
Annuities versus Single PaymentsTo go from single payments in Chapter 9 to annuities in this chapter, you need to make several adaptations: Annuity Payment Amount (PMT). Annuity calculations require you to tie a value to this variable in the formulas and when you use technology such as the BAII+ calculator. Payment Frequency or Payments per Year (P/Y). When you work with annuities, an actual value for P/Y is determined by the payment frequency. For simple annuities P/Y remains the same as C/Y, whereas the variables are different for general annuities. Cash Flow Sign Convention on the Calculator. It now becomes critical to ensure the proper application of the cash flow sign convention on the calculator—failure to do so will result in an incorrect answer. For example, if you borrow money and then make annuity payments on it, you enter the present value (PV) as a positive (you received the money) while you enter the annuity payments as negatives (you paid the money to the bank). This results in future balances getting smaller and you owing less money. If you inadvertently enter the annuity payment as a positive number, this would mean you are borrowing more money from the bank so your future balance would increase and you would owe more money. These two answers are very different! Definition and Computation of n. When you worked with single payments, [latex]n[/latex] was defined as the total number of compounds throughout the term of the financial transaction. When you work with annuities, [latex]n[/latex] is defined as the total number of payments throughout the term of the annuity. You calculate it using Formula 11.1 below. The Formula[latex]\colorbox{LightGray}{Formula 11.1}\; \color{BlueViolet}{\text{Number of Annuity Payments:}\; n=P/Y \times \text{Number of Years}}[/latex] where, n is the total number of annuity payments. How It WorksOn a two-year loan with monthly payments and semi-annual compounding, the payment frequency is monthly, or 12 times per year. With a term of two years, that makes n = 2 × 12 = 24 payments. Note that the calculation of n for an annuity does not involve the compounding frequency. Adapting Timelines to Incorporate AnnuitiesA good annuity timeline should illustrate the present value (PV), future value (FV), number of annuity payments (n), nominal interest rate (I/Y), compounding frequency (C/Y), annuity payment (PMT), and the payment frequency (P/Y). One of these variables will be the unknown. What type of an annuity where the payment interval is the same as the interest period?The main difference is that in a simple annuity the payment interval is the same as the interest period while in a general annuity the payment interval is not the same as the interest period.
Is an annuity where the payment interval is the same as the interest compounding period?Simple Annuity Due
Payments are made at the beginning of the payment intervals, and the payment and compounding frequencies are equal.
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