# Math Help - Trying to find time period for portfolio growth

1. ## Trying to find time period for portfolio growth

Hi all,

Trying to calculate for different portfolio growth, and the time period required to reach a sum, the equation looks something like this

100(1.08)^x + 200 (1.07)^x + 300 (1.01)^ x >= 2000

Solve for x, of which ^ means to the power to and x is time period.

Thanks!

2. ## Re: Trying to find time period for portfolio growth

Originally Posted by Yew
Hi all,

Trying to calculate for different portfolio growth, and the time period required to reach a sum, the equation looks something like this

100(1.08)^x + 200 (1.07)^x + 300 (1.01)^ x >= 2000

Solve for x, of which ^ means to the power to and x is time period.

Thanks!
Hi yew,

Your question is not basically about portfolio management. Portfolio management will generally involve Beta factor, standard deviation, risk free rate....so on. Even I don't think this question can be classified as business math. This question basically involves the use of the compound interest rate formula. But if you insist to call this a business math question , then the concept you are talking about is FV i.e future value of annuity. The first amount 100(assuming it is a scrip) bears an interest rate of 8%, the second scrip 200 bears an interest rate of 7% and the third scrip 300 bears an interest rate of 1%. There is no further information-whether the interest rates are annual or monthly etc. Nevertheless assuming x as one time period you can easily calculate the cash flow for each scrip separately and then check by adding the compound value of the three scrips where the sum equals or exceeds 2000. You can use calculator or FVIF (future value interest factor for annuity) Table for speedy calculations.

3. ## Re: Trying to find time period for portfolio growth

Originally Posted by Yew
Hi all,

Trying to calculate for different portfolio growth, and the time period required to reach a sum, the equation looks something like this

100(1.08)^x + 200 (1.07)^x + 300 (1.01)^ x >= 2000

Solve for x, of which ^ means to the power to and x is time period.

Thanks!
I do not know a formula to solve this problem. You must use some numeric method. I get $x \approx 24.$

4. ## Re: Trying to find time period for portfolio growth

Hi JeffM, thanks.... A numeric method, does it mean that we have to start from 1 to in this case about 24, in order to derive the x via a trial and error method? Thanks.

5. ## Re: Trying to find time period for portfolio growth

Originally Posted by Yew
Hi JeffM, thanks.... A numeric method, does it mean that we have to start from 1 to in this case about 24, in order to derive the x via a trial and error method? Thanks.
A numerical method is a way of approximating an answer for which no closed form provides the answer. The study of such methods is a particular branch of math that has exploded since the advent of computers. Many of those methods involve sophisticated trial and error, in that each trial is very likely to be a better approximation than the preceding trial and the approximations are very likely to become very accurate in a small number of trials. Quite possibly one of those methods would give a good approximation in three or four trials, but I just wrote an excel spread sheet and did it by having the computer try it for 1 through 100 iterations. Not elegant, but the computer does 100 iterations before you can blink.