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Annuities
An Annuity is a bunch of structured payments or equal payments made regularly, like every month or every week.
You win the lottery. The lottery guy comes to your house and says you have to choose between getting $ 1,000,000 now in one lump sum, or getting structured payments of $ 50,000 a year for the next 22 years. Which do you take?? Or, similarly, let's say you were injured on the job or whatever and were awarded an annuity of structured payments of $50,000 a year for the next 22 years. Perhaps you want to sell your annuity (the payments) to someone and get a lump sum of cash today. Is it worth $1,000,000?
First you have to choose an interest rate. Money is generally worth less in the future, right? So that $50,000 payment you get in 22 years is not going to be worth as much as it is today? You know, stuff will be more expensive then, right? So guess an interest rate, in this case, the rate of inflation for the next 22 years. Lets say 4%. Now, you have to figure out what is the present value of the $50,000 times 22 years discounted by 4% and then compare it with the million bucks. There are basically 2 ways to do this.
- Use a financial calculator.
- Use an annuity table.
Use a financial calculator - The PV of an Annuity.
- Enter n (the number of compounding periods - in this case the number of years). Press 22 and then push the N button.
- Enter i (the interest rate per period - in this case the number of years). Press 4 and then push the i button.
- Enter FV (the future value). It is zero. You want to know the Present Value, not the future value, right? Push 0 and then push the FV button.
- Enter PMT (the payment). You are not making a payment, you are getting one. So you have to show a negative number. Press 50000, then the CHS (change sign button), then push the PMT button.
- Push the PV (present value) button.
- Answer = $722,555. This means 22 annual structured payments of 50,000 each is worth only $722,555 of today's dollars. So you should take the million bucks from the lottery guy in one lump sum.
Use an annuity table - The PV of an Annuity.
Somewhere in your book, I bet there is a table that looks something like this:
| 1% | 2% | 3% | 4% | |
| 1 | 00.9901 | 00.9804 | 00.9703 | 00.9615 |
| 2 | 01.9704 | 01.9416 | 01.9135 | 01.8861 |
| 3 | 02.9410 | 02.8839 | 02.8286 | 02.7751 |
| 4 | 03.9020 | 03.8077 | 03.7171 | 03.6299 |
| 5 | 04.8534 | 04.7135 | 04.5797 | 04.4518 |
| 6 | 05.7955 | 05.6014 | 05.4172 | 05.2421 |
| 7 | 06.7282 | 06.4720 | 06.2302 | 06.0021 |
| 8 | 07.6517 | 07.3255 | 07.0197 | 06.7327 |
| 9 | 08.5660 | 08.1622 | 07.7861 | 07.4353 |
| 10 | 09.4713 | 08.9826 | 08.5302 | 08.1109 |
| 11 | 10.3676 | 09.7868 | 09.2526 | 08.7605 |
| 12 | 11.2551 | 10.5753 | 09.9450 | 09.3851 |
| 13 | 12.1337 | 11.3484 | 10.6350 | 09.9856 |
| 14 | 13.0037 | 12.1062 | 11.2961 | 10.5631 |
| 15 | 13.8651 | 12.8493 | 11.9379 | 11.1184 |
| 16 | 14.7179 | 13.5777 | 12.5611 | 11.6523 |
| 17 | 15.5623 | 14.2919 | 13.1661 | 12.1657 |
| 18 | 16.3983 | 14.9920 | 13.7535 | 12.6593 |
| 19 | 17.2260 | 15.6785 | 14.3238 | 13.1339 |
| 20 | 18.0456 | 16.3541 | 14.8775 | 13.5903 |
| 21 | 18.8570 | 17.0112 | 15.4150 | 14.0292 |
| 22 | 19.6604 | 17.6580 | 15.9369 | 14.4511 |
- Find this table.
- On the left, find the number of compounding periods (in this case years) - 22
- On the top, find the interest rate - 4%
- Find below where they meet. It says 14.4511
- Multiply 14.5111 times the Payment - $50,000
- Answer = $725,555. This means 22 annual structured payments of 50,000 each is worth only $722,555 of today's dollars. So you should take the million bucks from the lottery guy in one lump sum.