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## How to Calculate the Time Value of Money

**By JLP** | December 12, 2005

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.

Tags: Net Present Value, Present Value, Present Value of an Annuity, How to Calculate Present Value of an Annuity, How to Calculate Present Value

**Topics:** Basics, Financial Planning, Time Value of Money | 9 Comments »

January 2nd, 2006 at 9:10 pm

Carnival of Investing #3Welcome to Consumerism Commentary, this week’s host of the Carnival of Investing! The Carnival of Investing is a new Blog Carnival that collects the best blog entries in the past week or so that focus on the topic of investing. In the words of Mr…

January 3rd, 2006 at 11:59 am

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.

March 15th, 2006 at 8:02 pm

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.”

April 20th, 2006 at 5:41 pm

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?

April 23rd, 2006 at 10:50 pm

Troy

This calculator assumes 7.5%, but it will give you an idea!

BarbermanRetirement Calculatorhttp://www.bankrate.com/brm/calculators/investing.asp

Your ResultsRequired 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

June 12th, 2006 at 10:47 pm

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

October 19th, 2006 at 12:22 am

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

September 13th, 2008 at 4:37 pm

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

Thank you for sharing.

August 31st, 2010 at 4:01 pm

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.