Question

1. Today is your 25^th birthday. Your goal is to retire when you turn 70 years old and have sufficient monthly income until your expected demise on your 99^th birthday. In order to realize your goal, you are planning to make deposits into a target-date retirement fund that is expected to generate 7.8% annual return, compounded monthly. You want to be able to make monthly withdrawals from this fund starting one month after your retirement until your expected demise. These monthly withdrawals will increase by 0.3% a month in order to compensate for the expected increase in price levels. Retirees are able to survive on $2,000 monthly income today. Your first withdrawal one month after your 70^th birthday, therefore, will be $2,000 adjusted for 0.3% expected monthly inflation.

1. You are planning to make equal annual deposits starting one year from today until you retire. Calculate your deposits.
2. You are planning to make annual deposits starting one year from today until you retire. However, you believe that you can increase your deposits 4% a year in line with the expected increase in your income. Calculate your first deposit.
3. You are expecting inheritance money in the amount of $200,000 when you turn 50 years old and planning to deposit this amount immediately into the fund. Based on this expectation, recalculate your answer to part b.

Answer 1

		Number of years to retirement	45	(70-25)
		Number of months to retirement	540	(45*12)
		Number of months to first withdrawal	541
		Monthly income required today	$2,000
		Monthly inflation=0.3%=	0.003
		First monthly withdrawal required considering inflation	$10,112	(2000*((1+0.003)^541))
		Monthly Inflation rate	0.003
		Monthly nominal return=(7.8/12)%=	0.0065
		Assume Inflation Adjusted Return=r
		(1+r)=(1+0.0065)/(1+0.003)	1.003489531
	Rate	Inflation adjusted return (Real return)=	0.003489531
	Nper	Number of withdrawals	348	(99-70)*12
	Pmt	Monthly withdrawal at constant dollar	$10,112
	PV	Present Value of withdrawals at age of 70	$2,035,616	(Using PV function of excel with Rate=0.0034895, Nper=348, Pmt=-10112)
	a.	EQUAL ANNUAL DEPOSIT RQUIRED STARTING ONE YEAR FROM TODAY
	Nper	Number of years to retirement	45
	Rate	Annual Interest Rate=7.8%	0.078
	Fv	Future Value Required	$2,035,616
	PMT	Annual Deposit Required	$5,597.49	(Using PMT function of excel with Rate=0.078, Nper=45,Fv=-2035616)
	b	ANNUAL DEPOSIT REQUIRED (INCREASING AT 4%)STARTING ONE YEAR FROM TODAY
		Future Value of first deposit of $1 increasing at 4% for 45 years:
		N	A	B=A*(1.078^(45-N))
		Year	Deposit	Future value of deposit at end of 45 years
		1	$1	27.2412
		2	$1.04	26.2809
		3	$1.08	25.3545
		4	$1.12	24.4607
		5	$1.17	23.5985
		6	$1.22	22.7666
		7	$1.27	21.9641
		8	$1.32	21.1898
		9	$1.37	20.4429
		10	$1.42	19.7223	43 $5.19 6.0345 44 $5.40 5.8217 45 $5.62 5.6165 SUM 619.0733345 First Deposit Required=(2035616/619.0733345)= $3,288.17 Future Value of inheritance at retirement: Amount of inheritance $200,000 Annual Interest =7.8%= 0.078 Years to retirement 20 (70-50) Future Value of inheritance at retirement= $          898,267 (200000*(1.078^20) Balance savings required at retirement= $1,137,350 (2035616-898267) First Deposit Required =(1137350/619.0733345)= $1,837.18