It is amazing how the math we all thought was useless back in high school is really pretty useful today. Understanding mathematical concepts is very important in understanding personal finance. It is also very liberating to be able to do different “complex” calculations with the aid of a spreadsheet.

Today I want to show you how to calculate the present value of an annuity stream. Huh? Well, before you zone out or click away from this post, let me start with a question: Say you want to live on \$50,000 per year from your investments once you retire. Let’s say you are going to retire at age 60 and expect to need the money for 25 years. We will also say that you expect to get a 5% return on your money. Now, how much money do you need at age 60 to be able to meet your goal?

Well, if you were to put all your money under your mattress where it got zero return, you would need \$1,250,000 (\$50,000 X 25 years = \$1,250,000). You would stick \$1,250,000 under your mattress and each year take out \$50,000 to spend. At the end of 20 years, you would have nothing left.

However, if you are like most people, you probably want to get some sort of return on your money. This makes the calculation more difficult but not impossible. As we said earlier, let’s say you expect to get 5% per year on your money. To do this calculation, we have to use the following formula:

(1/i) – [1/(i X (1 + i)n)]

The “i” stands for expected interest rate, which is 5% (.05). The “n” stands for the number of periods, which is 25 years. The “X” is the multiplication sign. So, using real numbers, the equation would look like this:

(1/.05) – [1/(.05 X (1 + .05)25)]

20 – [1/(.05 X 3.3863549]

20 – [1/.1693177]

20 – 5.9060554

14.0939446

14.0939446 is our “factor.” To get the amount of money we need at age 60 to fund this income stream, you multiply \$50,000 by the factor (14.0939446). So, for this example, we need \$704,697 in the bank at age 60 in order to fund an annual income of \$50,000 for 25 years. IMPORTANT NOTE: At the end of 25 years, the money will be gone!

Was this helpful? Let me know by leaving any questions or comments. In a future post, I’ll show you how to do this same calculation with a spreadsheet.

UPDATE: Here’s a link to a follow-up post to this one.

### 9 responses to How to Calculate the Time Value of Money

1. I’d like to have enough money so that I will not have to eat into the principal at retirement just in case I live too
long. Most people use 4% as a safe withdrawal rate, but 3% would be more conservative.

2. A man is trying to understand the nature of God and asked him: “God, how long is a million years to you?”

God answered: “A million years is like a minute.”

Then the man asked: “God, how much is a million dollars to you?” And God replied: “A million dollars is like a penny.”

Finally the man asked: “God, could you give me a penny?” And God says: “In a minute.”

3. I am planning to retire 10 years from today. I want to have enough money set aside to allow me to draw \$2,000 per month for 20 consecutive years after I retire. I currently have \$50,000 in my savings account. Approximately, how much do I have to deposit each month into my account to be able to retire 10 years from now? Assume I can earn 6% per year.

Can you help with this calculation? and How?

4. Troy
This calculator assumes 7.5%, but it will give you an idea!
Barberman
Retirement Calculator

http://www.bankrate.com/brm/calculators/investing.asp

Required Income (Current Dollars) \$24,000.00
Required Income (Future Dollars) \$24,000.00
Number of Years Until Retiring 10
Number of Years After Retiring 25
Annual Inflation (on Required Income) 0.00%
Annual Yield on Balance 7.50%
You will need \$287,591.20 (\$139,537.51 invested today)
Year Beg.Bal. Withdraw Interest End Bal.
1 287,591.20 24,000.00 19,769.34 283,360.54
2 283,360.54 24,000.00 19,452.04 278,812.58
3 278,812.58 24,000.00 19,110.94 273,923.53
4 273,923.53 24,000.00 18,744.26 268,667.79
5 268,667.79 24,000.00 18,350.08 263,017.88
6 263,017.88 24,000.00 17,926.34 256,944.22
7 256,944.22 24,000.00 17,470.82 250,415.03
8 250,415.03 24,000.00 16,981.13 243,396.16
9 243,396.16 24,000.00 16,454.71 235,850.87
10 235,850.87 24,000.00 15,888.82 227,739.69
11 227,739.69 24,000.00 15,280.48 219,020.17
12 219,020.17 24,000.00 14,626.51 209,646.68
13 209,646.68 24,000.00 13,923.50 199,570.18
14 199,570.18 24,000.00 13,167.76 188,737.94
15 188,737.94 24,000.00 12,355.35 177,093.29
16 177,093.29 24,000.00 11,482.00 164,575.29
17 164,575.29 24,000.00 10,543.15 151,118.43
18 151,118.43 24,000.00 9,533.88 136,652.31
19 136,652.31 24,000.00 8,448.92 121,101.24
20 121,101.24 24,000.00 7,282.59 104,383.83
21 104,383.83 24,000.00 6,028.79 86,412.62
22 86,412.62 24,000.00 4,680.95 67,093.56
23 67,093.56 24,000.00 3,232.02 46,325.58
24 46,325.58 24,000.00 1,674.42 24,000.00
25 24,000.00 24,000.00 -0.00 -0.00

5. CURRENTLY I AM IN A FIN CLASS ONLINE. I HAVE NEVER TAKEN FIN AND THIS WAS VERY HELPFUL. MY CURRENT ASSIGNMENTS ASK ME TO CALCULATE TMV AND PROVIDE EXCEL TMV FORMULAS. YOU MENTIONED YOU COULD PUT THE EXAMPLES IN A SPREADSHEET. I WOULD BE VERY INTERESTED IN SEEING THAT AS IT WOULD BE HELPFUL WITH THIS WEEKS ASSIGNMENT.

THANK YOU

6. http://www.financescholar.com/timevalueofmoney.html offers description of Present Value, Future Value and Compounding Interest with custom made graphs:

7. This example helped me to understand. It was easy to follow along and I don’t enjoy math.

Thank you for sharing.

8. This was sort of helpful. I was trying to figure out how to enter a calcuation into an excel speadsheet so I could use it as a TVM calculator and change the variables as needed. Can you offer any help there? The pre done formulas seem to only solve for one variable.