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Time Value of Money
Annuities
Perpetuities
Kinds of Interest Rates
Future Value of an Uneven Cash flow
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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.

  1. Enter n (the number of compounding periods - in this case the number of years). Press 22 and then push the N button.
  2. Enter i (the interest rate per period - in this case the number of years). Press 4 and then push the i button.
  3. 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.
  4. 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.
  5. Push the PV (present value) button.
  6. 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
  1. Find this table.
  2. On the left, find the number of compounding periods (in this case years) - 22
  3. On the top, find the interest rate - 4%
  4. Find below where they meet. It says 14.4511
  5. Multiply 14.4511 times the Payment - $50,000
  6. 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.







About the author

Mark McCracken

Author: Mark McCracken is a corporate trainer and author living in Higashi Osaka, Japan. He is the author of thousands of online articles as well as the Business English textbook, "25 Business Skills in English".

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