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I am trying to find a formula that will let me calculate what percentage my money will need to grow at to reach my goal at the end of ten years, if I start with a certain amount and keep contributing a set amount to that portfolio for each month over the ten-year period. The only growth rate formulas I know deal with a fixed amount growing to another amount--as far as I know, these formulas don't take into account any money that might be donated to the portfolio along the way.

For example, the Drip Port's goal was to start with $500, contribute $100 each month for 20 years (for a total of $24,500 contributed after 20 years), and have the value of the portfolio grow to $150,000 by the end of that 20 years. But this isn't the same as starting the portfolio with $24,000 and calculating what percentage that amount will need to grow at for 20 years to reach $150,000. Jeff (or whoever wrote the Drip Port introduction) calculated that the portfolio would have to grow by 15.5% each year in order to reach this goal, but what formula was used to calculate this percentage?

If anyone knows a formula I can use to calculate this, or can point me to another message on this board that might help me (I'm sure this question has come up before) I'd appreciate it. Thanks!

myadidas
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I am trying to find a formula that will let me calculate what percentage my money will need to grow at to reach my goal at the end of ten years, if I start with a certain amount and keep contributing a set amount to that portfolio for each month over the ten-year period.

What you're looking for is called a "time value of money" calculation. Unfortunately, calculating TVM is not easy, and you need a specialized business calculator (or computer application) to do so with any reasonable ease. There are some such calculators online, though. For example, http://147.4.150.5/~matscw/RealWorld/tmvcalc.html
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ma,

I am trying to find a formula that will let me calculate what percentage my money will need to grow at to reach my goal at the end of ten years, if I start with a certain amount and keep contributing a set amount to that portfolio for each month over the ten-year period. The only growth rate formulas I know deal with a fixed amount growing to another amount--as far as I know, these formulas don't take into account any money that might be donated to the portfolio along the way.


Do you have a financial calculator?

If you know any four of the following you can solve for the fifth:

1. Present Value (PV)
2. Future Value (FV)
3. Periodic Payment (PMT)
4. Nominal Interest Rate (I/YR); and
5. Number of Compounding Periods (N)

I use a Hewlett Packard 10B. Set your calculator appropriately to whether you'll be making payments at the beginning or end of the month. I'll give the symbols that appear on my calculator.

So:

1. Enter your present value (PV)
2. Enter the future value as a negative number (FV)
3. Enter 12 payments per year (P/YR)
4. Enter number of years (xP/YR)
5. Enter amount of monthly payment (PMT), then

6. Solve for nominal interest rate (I/YR)

Hope this helps.

OB

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Well,

its also not a very hard statistical formula. I believe just about anyone whose taken statistcs at University should be able to do.

Basically, you are trying to find the Future value of an Annuity (or "amount" value). Take into consideration monthly payments (12payments/year), for 10 years. The compound amount of the last payment (what you have after 10 years) is S, and that you are making "n" paymments, at interest rate r, and each payment is "R".

Then the formula is:
S = R * [(1 + r)^n - 1]/r

Therefore, assume you are investing monthly payments of $50, at a rate of 15% per year, compounded monthly.

Then

R = 50
r = .15/12 = 0.0125 (divide by 12 because you are "compounding" 12 times throughout the year).
n = 12(10) = 120 payments all togehter

Then, working it out..

S = 50 * [(1.0125)^120 - 1]/0.0125
works out to:

S =
$ 13,760

Therefore, if you invest $50/month for 10 years, at a rate of 15%/year, you will have after 10 years $13,760 (with an investment of 50*120 = 6000).

So, essentially you make $13760 - 6000 = $7760 after 10 years.

Hope it makes some sense :)


Andrew.
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Andrew,

Problem is he's starting with a lump sum I believe and with monthly payments vs. annual. In this case the formula is more convoluted.

OB
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ah ha..
didn't read his actual message, just your replies.

It's not hard to adjust the formula for an initial lump sum (add 1 variable). Also, i believe my example was monthly payments? (and tha'ts what he wanted i assume).

So the only thing i need to adjust is an initial lump sum?
if so, no problem. It's a very well known formula.

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I have to admit I just use calculators on the internet to figure this out. I was never very good with math and formulas tend to confuse me.

The calculator I use most frequently is at www.timevalue.com and it shows the following.

$24K at 15% for 20yrs = $473,171

$500 plus $100 month at 15% for 20yrs = $159,581

the calculator also shows how many months this money will last as different withdrawal rates. For example,

$473,171 earning 6.9% can provide $3619 for 240 months, OR,
$473,171 earning 6.9% can provide $2720 indefinately.

$159,581 earning 6.9% can provide $1220 for 240 months, OR,
$159,581 earning 6.9% can provide $917 indefinately.

Hope this helps and have fun.
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If you are not starting with a lump sum, you can probably use the calculator on my site (http://members.home.net/hmpi/Invest/DRiPInvesting.htm). Just select the Future Value of Regular Investments link.

Cheers -

george
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Thanks to everyone for responding! Unfortunately, I don't have a business type calculator (though I should probably get one, since I plan to apply to business school!), so I'll go download George's spreadsheet and check the websites some of you gave me to use.

myadidas
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It's not hard to adjust the formula for an initial lump sum (add 1 variable). Also, i believe my example was monthly payments? (and tha'ts what he wanted i assume).

So the only thing i need to adjust is an initial lump sum?
if so, no problem. It's a very well known formula.


andmunn,

I was looking for a formula that would allow me to start with a lump sum, keep adding a set amount of money to that lump sum each month, and then calculate what I would have at the end.

I looked at the formula you included in your other message, but couldn't figure out where a lump sum could be inserted in that equation. Do you know where it would go?

In the meantime, I went to the first link and entered in the information to see how long it would take for me to reach the target amount I had set for the ten year mark--as I suspected, I had underestimated how long it would take me to reach my goal!! By about, well, 2 1/2 years.

And I was only using the average growth rate of the S&P 500 (11% per year). Since I'm hoping to beat the S&P 500 with my drip portfolio, it looks like I should set my goal slightly bigger than it is now.

Thanks to everyone again!

myadidas
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ma,

This is the closest formula I could get from my Canadian Financial Planning Institute and it doesn't cover a lump sum to start. As I said it's convoluted:

Future Value of an Annuity Due

FV = (1+ (I/YR*P/YR))xPMTx [((1+(I/YR * P/YR))^N - 1) * (I/YR * P/YR)]

P/YR = # of compounding periods and payments per year
N = # of compounding or discounting periods and payments
I/YR = nominal annual interest rate
PV = Present Value
FV = Future Value
PMT = Payment
* = divided by here (because of use of "/"in abbreviations)
^N = the power of "N"

If you're comfortable with it you could e-mail one of us, with access to a financial calculator, your proposed figures and we could calculate it for you.

OB

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"PV" actually covers the "lump sum" at the start of the investment, so this seems to be the right formula to use. What makes it difficult is that, if the unknown is the interest rate, there is no known efficient method of solving such an equation in general. If you wanted to do it by hand, you have to essentially use "trial and error" (binary search) techniques for the rate.

The "magic" that happens in a financial calculator is that it does this trial and error automatically for you.
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Foobar,

Right you are. Only thing is the formula I gave doesn't have a symbol for "PV" in it. It only shows "FV".

One possibility is to calculate the lump sum as a future value and then calculate the payments as an "annuity due". Then add the two together. Quite possibly that's what a financial calculator does anyway.

Wha'd'ya think?

OB
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I guess I was asleep at the wheel, for missing that. :( Yes, just adding them together is appropriate, and I believe that's how the calculators do it too.
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ma,

This is the closest formula I could get from my Canadian Financial Planning Institute and it doesn't cover a lump sum to start. As I said it's convoluted:

Future Value of an Annuity Due

FV = (1+ (I/YR*P/YR))xPMTx [((1+(I/YR * P/YR))^N - 1) * (I/YR * P/YR)]


OB,

You weren't kidding about how this equation looks! Thanks for finding this for me...I was able to get the information I needed from the website listed in the first response to my question, so no need for me to e-mail you my figures--it would have been nice to work through the equation myself though.

Guess I need to get a more powerful calculator...maybe I'll press my sock puppets to start producing more lint so that I can sell it to raise funds.

myadidas
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