If you invest $ 9,000 today, how much will you

In 25 years at 14 percent ( compounded semiannually)?
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How to calculate ?

You've got four methods by which to do this: charts/tables, algebraic equations, financial calculator and Excel. Are you required to use any one in particular or did you have a preference?

In general, you always need to decide if you are solving for a present value or a future value. Then you need to decide if it's a lump sum or a series of payments (annuity). That will not change from method to method. But how you handle compounding can make a difference with the method you use.

from the question what I will (have) so I would assume it's a calculation for the future.
here is the basic calculation

FV =$10,000 ,n=25 , I=6%
FVIF using table 26.462
FV = PV x FVIF $238,158

My question is how to calculate the compounded semiannually

from the question what i will (have) so i would assume it's a calculation for the future.
here is the basic calculation

FV =$10,000 ,n=25 , i=6%
FVIF using table 26.462
FV = PV x FVIF $238,158

You are not solving for a future value. You already have the future value - $10,000. A present value grows into a future value, and since you have the future, you're solving for what that present value is. I also don't know where that 26.462 is coming from. I have tried various combinations of things you may have done and cannot get that. So I'm not sure what chart you are using or what you are looking up on it. The FVIF implies a lump sum future value chart, but that factor is nowhere near as big as 26.462.


My question is how to calculate the compounded semiannually

Since it compounds twice a year, you have to do it by periods, not years. However, the n and i can stand for various things, depending on the book. On those charts, generally i represents the interest per compounding period (i.e. for semiannual that would be per every 6 months), and n represents the number of periods. If that is how your charts are doing it, it's already set up that way.