Investment

Question

your traditional IRA account has stock of GFH, which cost $2000, 20 year ago when you were 50 year old. you have been very fortunate, and the stock is now worth $23,000. you are in the 35 percent income tax bracket and pay 15 percent on long-term capital gains.

 

What was the annual rate of growth in the value of the stock?

 

What are the taxes owed if you withdraw the funds?

 

 

Answer 1

I like to start these problems with the base formula, FV=PV(1+i)ⁿ. This way, I don't have to remember a lot of formulas. In this case, FV=23000, PV=2000, n=20 years, and we need to find i. We can move this formula around to be:

FV/PV=(1+i)ⁿ

If we take the 20th root of both sides, we get:

(FV/PV)^-20 = (1+i)¹

(23000/2000)^-20=1+i

1.130 = 1+i

i=0.13, or 13%. You can check your work by plugging 13% back into the original formula: FV=2000(1+0.13)²⁰ = $23,046.18. The $46.18 is due to rounding of i.

So the annual growth rate of the stock is 13% -- a very good rate of return.

Since it is in an IRA, it would not be subject to capital gains upon sale of the stock. Once the funds are withdrawn from the IRA, it is considered regular income, and taxed in this case at the person's tax rate of 35%. So the tax on the withdrawal would be 23000*35% = $8050.