The formula to calculate the Annuity Payment is:
\[ \text{Annuity Payment} = \frac{\text{Rate per Period} \times \text{Present Value}}{1 - (1 + \text{Rate per Period})^{-\text{Number of Periods}}} \]
Where:
Annuity Payment is a series of payments at fixed intervals, guaranteed for a fixed number of years or the lifetime of one or more individuals.
Let's assume the following values:
Using the formula:
\[ \text{Annuity Payment} = \frac{0.5 \times 10}{1 - (1 + 0.5)^{-2}} \]
Evaluating:
\[ \text{Annuity Payment} = \frac{5}{1 - (1.5)^{-2}} \]
\[ \text{Annuity Payment} = \frac{5}{1 - 0.4444444444444444} \]
\[ \text{Annuity Payment} = \frac{5}{0.5555555555555556} \]
\[ \text{Annuity Payment} = 9 \]
The Annuity Payment is 9.
| Rate per Period (%) | Present Value | Number of Periods | Annuity Payment |
|---|---|---|---|
| 0.5% | 10 | 2 | 5.037531172070 |
| 0.5% | 10 | 3 | 3.366722083565 |
| 0.5% | 10 | 4 | 2.531327929787 |
| 0.5% | 10 | 5 | 2.030099749755 |
| 0.5% | 15 | 2 | 7.556296758105 |
| 0.5% | 15 | 3 | 5.050083125347 |
| 0.5% | 15 | 4 | 3.796991894680 |
| 0.5% | 15 | 5 | 3.045149624633 |
| 0.5% | 20 | 2 | 10.075062344140 |
| 0.5% | 20 | 3 | 6.733444167130 |
| 0.5% | 20 | 4 | 5.062655859574 |
| 0.5% | 20 | 5 | 4.060199499510 |
| 1% | 10 | 2 | 5.075124378109 |
| 1% | 10 | 3 | 3.400221114815 |
| 1% | 10 | 4 | 2.562810939117 |
| 1% | 10 | 5 | 2.060397996159 |
| 1% | 15 | 2 | 7.612686567164 |
| 1% | 15 | 3 | 5.100331672222 |
| 1% | 15 | 4 | 3.844216408675 |
| 1% | 15 | 5 | 3.090596994238 |
| 1% | 20 | 2 | 10.150248756219 |
| 1% | 20 | 3 | 6.800442229629 |
| 1% | 20 | 4 | 5.125621878233 |
| 1% | 20 | 5 | 4.120795992318 |
| 1.5% | 10 | 2 | 5.112779156328 |
| 1.5% | 10 | 3 | 3.433829602082 |
| 1.5% | 10 | 4 | 2.594447859881 |
| 1.5% | 10 | 5 | 2.090893230951 |
| 1.5% | 15 | 2 | 7.669168734491 |
| 1.5% | 15 | 3 | 5.150744403123 |
| 1.5% | 15 | 4 | 3.891671789822 |
| 1.5% | 15 | 5 | 3.136339846427 |
| 1.5% | 20 | 2 | 10.225558312655 |
| 1.5% | 20 | 3 | 6.867659204164 |
| 1.5% | 20 | 4 | 5.188895719763 |
| 1.5% | 20 | 5 | 4.181786461903 |