Question

Complete these problems with steps:

1. Your mother just won $250,000 for splitting a Nobel Prize equally with three other co-workers. If she invests her prize money in a diversified equity portfolio returning 8 percent per year, approximately how long will it take her to become a millionaire, before accounting for taxes?

2. Jill received a 30,000 inheritance. She wants to save up for a down payment for her first home to be purchased 8 years from now. If she can earn 5% on her savings per year how much of the inheritance does she need to save now to make a $20,000 down payment 8 years from now?

3. Richard is 65 years old and about to retire. He has $500,000 saved to supplement his pension and social security and would like to withdraw his savings in equal dollar amounts so that nothing is left after 15 years. How much does he have to withdraw each year if he earns 7 percent on his money?

4. Monica, 22 just started working full time and plans to deposit $3,000 annually into a Roth IRA earning 12 percent interest compounded annually. How much would she have after 20 years, 30 years, and 40 years? If she decided to make monthly payments of $250 per month instead of the $3,000 each year would she end up with more or less money at the end of 40 years (assuming interest was compounded monthly)? If she had a 30% tax rate when she took the money out 40 years from now how much in taxes would she have to pay?

Answer 1

Question number 4:

Note that for monthly contributions, you need to divide the interest rate by 12 (12%/12 = 1%) to get the monthly rate, and also use months for time period rather than year (ie. 20 years x 12 = 240 months).

She would end up with more money in all three cases if she made monthly deposits vs. annual deposits. Also, since the problem says this is a Roth IRA, there would be no tax liability when the money is withdrawn. Deposits intoa Roth IRA are post-tax, and all earnings can be withdrawn after age 59 1/2 tax free.

Question number 3:

Let the annual withdrawal be A. Therefore,

$500,000 = A * [1 - (1 + 7%)^-15] / 7%

=> A = $54,897.31

Therefore, he has to withdraw $54,897.31 each year.

Question number 2 :

Required
Future value = $20000
N= 8 years
r = 5%
Finding out the Present value
Present value = Future value/(1+r)ⁿ
= $20000/(1+0.05)⁸
= $13536.79
Amount to be saved today to make the downpayment of $20000 in 8 years = $13536.79

Question number 1:

Principal amount = $250,000

We require 4 mulitplication to become millionare
	That means we require future value interest factor of minimum of 4
	Future value interest factor at8% for 18.02 years is					=1*(1+8%)^18.02
						4.002175
	Multiplying it with by 250000					=250000*4.002175
						1000544
	In 18.02 years she will become milliionaire