Question

 Tilly would like to invest ​$3,000

in​ before-tax income each year in a retirement account or in stock investments outside the retirement account. Tilly likes the stock investments outside the retirement account because they provide her with more flexibility and a potentially higher return. Tilly would like to retire in 25years. If she invests money in the retirement​ account, she can earn

7​% annually. If she invests in stock outside the​ account, she can earn 8​% annually. Tilly is in the 25​% marginal tax bracket.

a. If Tilly invests all her money in the retirement account and withdraws all her income when she​ retires, what is her income after​ taxes?

b. If Tilly invests all her money in stocks outside the​ account, what are her savings at​ retirement?

​(Hint​:

Remember that the income is taxed prior to​ investment.)

c. Assuming a capital gains tax rate of 15​%,

what is the​ after-tax value of the stock​ investments?

d. Should Tilly invest her money in the retirement account or in stocks outside the​ account?

a. If Tilly invests all her money in the retirement account and withdraws all her income when she​ retires, her income after taxes is

​$________

​(Round to the nearest​ dollar.)

Answer 1

Solution:

Pre tax income each year = 3000.

25% tax is applicable for tilly so, the after tax income comes to be = 3000 * (1- 25%) = 3000 * .75 = 2250

Tilly's retirement time = 25 years.

a) If tilly invests all the funds in retirement account @ 7% annually the after tax income can be achieved as:

We will make the use of our BA II plus professional calculator to calculate the future value of yearly investments made i.e.

Payments = 2250 , N = 25 years , I/Y = 7% , PV = 0 , FV =??

Inputting the values in the TVM row . . . we get the FV as :- 142310.3349

b) If tilly invests all the funds in stock @ 8% annually the after tax income can be achieved as:

We will make the use of our BA II plus professional calculator to calculate the future value of yearly investments made i.e.

Payments = 2250 , N = 25 years , I/Y = 8% , PV = 0 , FV =??

Inputting the values in the TVM row . . . we get the FV as :- 164488.3649

c) After capital gain tax : 164488.3649 is pre capital gain tax , after the tax the net income comes out to be:-

164488.3649 * (1 - 15%) = 164488.3649 * .85 = 139815.1102

d) Since the amount that tilly received under the retirement account is 164488.3649 and under stock investment after capital gain tax 139815.1102 and the retirement account amount is much higher than the stock investment , it will be really beneficial for tilly to keep the amount in the retirement account.