Question

Investment A

You are 25 years old, having just started working. You are considering a retirement plan for a retirement at the age of 65. You want to be able to withdraw $73,000 from your savings account on each birthday for 20 years following your retirement at the age of 65. Your first withdrawal will be on your 66th birthday. To achieve your goal, you intend to make equal annual deposits in a pension scheme which offers 7% interest per year.

According to the Investment A, you expect a lump sum of $ 100,000 from a family inheritance fund that you will receive on your 50th birthday. You will put this fund into the retirement savings account. Furthermore, you have invested in a portfolio what will be giving you $ 1,300 per year (from age 25 through age 65) which are to be added the retirement savings account as well.

If you begin making these deposits on your 25nd birthday and continue to make deposits until you are 65 (your last deposit will be made on your 65th birthday), what is the amount you are required to deposit annually to be able to make the desired withdrawals at retirement?

Investment B

Here you still have the same retirement plan in mind, in other words you want to be able to withdraw $73,000 from your savings account on each birthday for 20 years following your retirement at the age of 65. However, the investment criteria are different:

You have invested in a business which gives an annual net profit of $ 2,300 per year.
Furthermore, your employer will contribute $ 550 to the account per year as part of the company’s

profit-sharing plan starting from age 45 to 65. What amount must you deposit annually now to be able to make the desired withdrawals at retirement? Which investment will you choose and why?

Answer 1

		Years to retirement	40	(65-25)
		Length of retirement (in years)	20
		Desired annual retirement income	$73,000
		Inheritance at age 50	$100,000
		Annual interest rate	7%
		At retirement:
	A	Value of retirement income at age 65	$773,363	(Using PV Function of excel with Rate=7%,Nper=20,Pmt=73000
	B	Value of inheritance at age 65 (after 15 years)	$275,903	(Using FV Function of excel with Rate=7%,Nper=15,Pv=100000)
	C=A-B	Total needed at retirement=773363-275903	$497,460
	D	Required Annual Savings	$2,492	(Using PMT Function of excel with Rate=7%,Nper=40,Fv=-497460)
	E	Annual Savings from Portfolio	$1,300
	F=D-E	Amount required to deposit annually=2492-1300	$1,192
		INVESTMENT B
	A	Value of retirement income at age 65	$773,363
	B	Value of inheritance at age 65 (after 15 years)	$275,903
	G	Value of annual contribution of $550 at age 65	$22,548	(Using FV Function of excel with Rate=7%,Nper=(65-45)=20,Pmt=-550)
	H=A-B-G	Total needed at retirement	$474,912
	I	Required Annual Savings	$2,378.90	(Using PMT Function of excel with Rate=7%,Nper=40,Fv=-474912)
	J	Annual Profit saved every year	$2,300
	K=I-J	Amount required to deposit annually=	$78.90
		INVESTMENT B should be chosen
		It has lower annual deposit