Concept of Ordinary Annuity
An ordinary annuity represents a series of equal payments made at the end of consecutive periods. While the frequency of these payments can be as often as weekly, they are typically made monthly, quarterly, semi-annually, or annually. The counterpart to an ordinary annuity is the annuity due, where payments occur at the beginning of each period.
Key Insights
- An ordinary annuity involves regular payments at the end of each period, such as monthly or quarterly.
- An annuity due, conversely, has payments at the start of each period.
- Examples include quarterly stock dividends (ordinary annuity) and monthly rent (annuity due).
Understanding Ordinary Annuities
How Ordinary Annuities Operate
Take interest payments from bonds, typically made semiannually, or quarterly stock dividends that are steady over time – these are classic examples of ordinary annuities. The present value of an ordinary annuity is closely tied to prevailing interest rates.
With the time value of money principle, rising interest rates diminish an ordinary annuity’s present value, whereas declining rates boost it. This reflects the value based on potential earnings if invested elsewhere. Higher alternative interest rates yield lower annuity values.
Present Value Calculation Example
The present value of an ordinary annuity uses these variables:
- PMT = Periodic cash payment
- r = Interest rate per period
- n = Total periods
The formula is:
- Present Value = PMT x ((1 - (1 + r) ^ -n ) / r)
For instance, with $50,000 annual payments over five years and a 7% interest rate, the present value is:
- Present Value = $50,000 x ((1 - (1 + 0.07) ^ -5) / 0.07) = $205,010
Ordinary annuities have lower present values compared to annuities due, given similar conditions.
Present Value of an Annuity Due Example
In contrast, annuities due have payments made at period beginnings – say, rent payments made in advance. This affects valuation, as seen in the formula:
- Present Value of Annuity Due = PMT + PMT x ((1 - (1 + r) ^ -(n-1) / r)
For the above annuity example as an annuity due, we calculate:
- Present Value of Annuity Due = $50,000 + $50,000 x ((1 - (1 + 0.07) ^ -(5-1) / 0.07) = $219,360
Thus, annuities due generally hold higher present values than ordinary annuities due to earlier payment times.
Related Terms: Present Value, Future Value, Annuity Due, Time Value of Money.
