<< If I invested an amount of $10000 at the beginning of the year and contributed $1000 at the end of each month for the next 12 months and at the end of year if I have total $Y including principle and profit/loss, what's my rate of return for the year? >>

There's an answer, but no easy answer to that one. Sorry.

When payments are involved you'll need a "root finder" to solve for "i", the interest rate, in the TVM, Time Value of Money, equation.

You can either purchase a financial calculator that has the TVM equation in firmware or use spreadsheet software that supports the IRR, Internal Rate of Return, function. The good news is that every piece of spreadsheet software I've every played with supports the IRR function.

Let's work Neb2000us's example using the Microsoft Works spreadsheet.

Mth# ... NCF

0 ..... -10000

1 ...... -1000

2 ...... -1000

3 ...... -1000

4 ...... -1000

5 ...... -1000

6 ...... -1000

7 ...... -1000

8 ...... -1000

9 ...... -1000

10 .... -1000

11 .... -1000

12 ... 23000

IRR = 0.010240622

Annualized 0.130050706

13.0%

Notes:

Mth# ... is the month number.

NCF ... is the Net Cash Flow to you.

If you made a contribution, you paid cash OUT and it is a negative number.

If you can received or withdraw cash it is a positive number.

The "root finder" behind the IRR function will fail or give you the wrong answer if you get the signs of the cash flows wrong.

Specifics:

You contributed (paid out) $10,000 at the END of month number # 0, (if it's easier, think of this as the BEGINNING of month # 1, for example: 31-Dec-2002 ~ 1-Jan-2003).

At the end of months # 1 .. # 12 (Jan .. Dec) you contributed (paid out) $1,000.

At the end of month # 12 you can withdraw (at least on paper) $24,000. So the NET cash flow to you for the end of month # 12 is $23,000 { + $24,000 - $1,000 }.

The calculated IRR, internal rate of return, is based on the period between net cash flows, in this case, one month.

So an IRR = 0.010240622 is a monthly interest rate (or total return) of 1.024%.

To annualized the monthly rate: add one to it, raise that to the twelve power (12 months to a year) and subtract one.

Annualized = [ ( 1 + 0.010240622 ) ^ 12 ] - 1 = 0.1301 = 13.01%

Full feature spreadsheet software (Microsoft Excel and Lotus123) support yet another variant of IRR called XIRR. XIRR takes two argument lists; an array of NCFs and an array of dates, as input and calculates an annualized internal rate of return for irregular periods. Very nice, your contributions don't have to be made exactly one month apart.

OK, the same problem on a financial calculator.

I'm currently playing around with an Aurora Financial Manager FN1000, a ~$25 cheapie Chinese knock off of Hewlett-Packard's HP12C (which sells for ~$69).

[SHIFT] [CLEAR FIN] ... clears the financial registers.

[SHIFT] [END] ... payments occur at the end of the period.

12 [n] ... there will be twelve payments.

10000 [+/-] [PV] ... stores -$10,000 as the present value.

1000 [+/-] [PMT] ... stores -$1,000 as the periodic (monthly) payments.

24000 [FV] ... stores +$24,000 as the future value.

[i] ... calculates the periodic (monthly) interest rate.

... nine seconds later ...

1.0241

That's the monthly return in percent.

Annualize it. (Warning, this is in RPN, Reverse Polish Notation).

1 [X<->Y] [%] [+] 12 [Y^X] 1 [-]

answer: 0.1301 = 13.01%

If you do decide to buy a financial calculator check out the Texas Instruments Financial Analyst II. I believe I've seen it at Walmart for about $30. I used to push Hewlett-Packard's stuff, but, IMHO, the quality (or lack therein) no longer supports the premium price they ask. I'll stick with RPN only because I've been using it for more than 25 years now and think it is the best "language" f