Perpetuity
A perpetuity is series of payments that starts at a certain point in time and that continues forever.
The Perpetuity calculation
lets you calculate the present value of such a series.
Payments can be constant or can change with a fixed amount or with a fixed percentage.
To see the amortization schedule, select the Show Details command in the Calculation menu.
To toggle between date and year/period view, click the header of the first details column.
To change the start date, select the Start Date command in the Edit menu to open the Date Options dialog.
Input
| • nominal annual rate | |
| • compounding frequency | |
| • payment frequency | |
| • number of periods before the first payment: | |
| 0
= perpetuity due 1 = normal perpetuity 2...n = deferred perpetuity |
|
| • first payment in the series | |
| • periodic change: | |
| •
no change • percentage (positive or negative) • amount (positive) |
|
Results
| • present value |
| • total paid |
Note:
Values that cannot be calculated
are represented by the infinity symbol (
).
The present value result cannot be calculated if the periodic change is a positive percentage and it is greater than the effective periodic interest rate.
The total paid result can only be calculated provided the periodic change is a negative percentage.
Example
| • | A site is returning an annual rent of $5,000 per year, payable at the beginning of the year. It is expected that the rent will increase 6 % per year, on the average, forever. What is the present value of the site at 10 %?
Answer: $137,500. |
Related topics
| Nominal annual rate |
| Compound interest |
| Annuity |