Question

1. A woman is in the 25% marginal tax bracket, and is considering the tax consequences of investing $2000 at the end of the year for 30 years in a tax-sheltered retirement account, assuming that the investment earns 8% annually.

1. How much will her account total over 30 years if the growth in the investment remains sheltered from taxes?

B. How much will the account total if the investments are not sheltered from taxes?

Answer 1

Annual investment= $2000

Years (n)= 30

no taxes on income. So rate = 8%

Future value of ordinary annuity formula = P *{ (1+i)^n - 1 } /i

2000*(((1+8%)^30)-1)/8%

=226566.4222

If tax sheltered investment

After tax interest rate = interest rate*(1-tax rate)

8%*(1-25%)

6%

Future value of annuity = 2000*(((1+6%)^30)-1)/6%

=158116.3724

her account total over 30 years will be $226566.42  if the growth in the investment remains sheltered from taxes

her account total over 30 years will be $158116.37  if the growth in the investment are not sheltered from taxes