interest rate

Question

Your traditional IRA account has stock of GFH, which cost $2000 20 years ago when you were 50 years old.  You have been very fortunate, and the stock is now worth $23000.  You are in the 35 percent income tax bracket andpay 15 percent on long term capital gains.  a) what was the annual rate of growth in the value of the stocks?  b) what are the taxes owed if you withdraw the funds?

Answer 1

a) 12.9887%

 = FV(12.9887%,20,,-2000,1).. $23,000 stock fund value  

net appreciation in value (over $2,000 initial cost) is $21,000..

b) The stock fund traditional IRA in this question is subject to a 15% capital gains tax (on a net gain), when the fund is sold, traded, or exchanged.. calculating a 35% income tax is an estimated tax for that transaction only..

 

Answer 2

(a) 2000(1+R)^20 =23,000; Solving for R will give you the annual growth rate. In this case it is 12.99%. If you are using a scientific calculator or excel you can use the following functions: PV = -2000, FV =23,000, N = 20, Compute I/Y.

 

(b) In a traditional IRA, the taxes are paid during distributions. When you withdraw funds, everything is taxed as ordinary income.

 

Taxes Owed = 23,000*0.35 = $8,050. Note that you are taxed on the full 23,000 since the contributions are made pre-tax.

Answer 3

Remember the Compound Interest Formula:

A = P (1 + r/n)^(nt), where:

A = the final amount,

P = the original amount (principal),

r = annual interest rate,

n = number of times in one year that interest is calculated, and

t = time in years.

 

In Annual Rate of Growth problems we want to find r where we know:

A = the final amount,
P = the original amount (principal),
r = annual interest rate = ???,
n =1, and
t = time in years.

 

For this problem:

A = $23,000,
P = $2,000,
r = annual interest rate = ???,
n =1, and
t = 20 years.

 

a.)

A = P (1 + r/n)^(nt)

23000 = 2000 (1 + r)^20

Divide by 2000:

23/2 = (1 + r)^20

Raise both sides to the 1/20 th power:

(23/2)^(1/20) = 1 + r

r = (23/2)^(1/20) - 1

Use your calculator:

r ≈ 0.12988668820156 ≈ 12.99%

 

b.) You will owe:

23000*0.35 ≈ $8,050 in taxes because IRA distributions are treated as ordinary income and the original amount you invested was not taxed.