Question

Your aunt Maria is planning for retirement in 12 years. She currently has a portfolio made up of $50,000 in a money market savings account and $125,000 in a mutual fund. She receives an annual bonus from her current employer that she plans to deposit in the savings account at the end of each year for the next 12 years. The annual rates of return for the savings account and mutual fund, and the annual amount deposited in the savings account appear in the following table.

The annual rate of return on savings account  4.00 percent  

The annual rate of return on mutual fund  7.50 percent  

The end-of-year savings deposit for years 1 - 6  $2,500  

The end-of-year savings deposit for years 7 - 12  $5,000

Compute the total amount of money in Aunt Maria's portfolio when she retires at the end of 12 years. To accomplish this, you must show the following values:

1. The future value of the initial savings balance.

2. The future value of the initial mutual fund balance.

3. The future value of the annual deposits to the savings account over the 12-year horizon.

4. The total future value of the portfolio.

When she retires, suppose your aunt deposits the total amount of money determined in part (A) in a new account earning 5.00 percent annually. If she expects to live another 20 years once she retires, how much can she withdraw each month to end up with a zero balance in the account upon her death? Assume she receives the withdrawal at the end of each month.

Answer 1

1	Future Value of Initial Savings Account Balance = $50,000 * (1+0.04)^12
	Future Value of Initial Savings Account Balance = $50,000 * 1.6010
	Future Value of Initial Savings Account Balance = $80,051.61
2	Future Value of Initial Mutual Funds Balance = $125,000 * (1+0.075)^12
	Future Value of Initial Mutual Funds Balance = $125,000 * 2.3818
	Future Value of Initial Mutual Funds Balance = $297,722.45

3	Future Value of annual deposits to Savings Account = [$2500 * PVAF(4%,6Years)] + [$5000 * PVAF(4%,7-12Years)]
	Future Value of annual deposits to Savings Account = [$2500 * 5.2425] + [$5000 * 4.1425]
	Future Value of annual deposits to Savings Account = $13,106.25 + $20,712.5
	Future Value of annual deposits to Savings Account = $33,818.75

n	r	1+r	(1+r)^-n	1- [(1+r)^-n]	[1- [(1+r)^-n]] /r
6 Years	4%	1.0400	0.7903	0.2097	5.2425
12 Years	4%	1.0400	0.6246	0.3754	9.3850

PVAF(4%,7-12Years) = PVAF(4%,12Years) - PVAF(4%,6Years)

PVAF(4%,7-12Years) = 9.3850 - 5.2425

PVAF(4%,7-12Years) = 4.1425

4	Total value of Portfolio after 12 Years = 1+2+3
	Total value of Portfolio after 12 Years = $411,592.81

Pv of Annual Withdrawls	n = 20 yrs *12 Mts	I = 5%/12	1+i	(1+i)^-n	1- [(1+i)^-n]	PVAF = [1- [(1+r)^-n]] /r	Monthly Withdrawl
$     411,593	240	0.42%	1.0042	0.3686	0.6314	151.5360	$ 2,716