Question

Suppose Connie is now at the age of 34 and starts savings for her retirement at the age of 65. She wants to be able to withdraw $300,000 from her savings account on each birthday after her retirement, with the first withdrawal on her 66th birthday and the last withdrawal on her 88th birthday.

(a) She is considering joining a savings plan offered by Insurance Company A, which offers her a return of 10% p.a. throughout the entire period. Assume that she wants to make equal deposit into the savings account on each of her birthdays, with the first deposit on her 35th birthday and the last deposit on her 65th birthday. How much money does she need to deposit every year into the savings account in order to meet her retirement plan?

(b) Suppose Insurance Company B offers Connie another savings plan. According to this savings plan, she is required to make a fixed monthly deposit into her account, where she could earn 15% EAR. On her retirement date, all her money in the savings account will be transferred to a more liquid account paying 6% EAR, from which she could withdraw her money freely as she likes.

To take advantage of the liquidity of her account, Connie is planning to make the following withdrawals in addition to her annual withdrawals of $300,000 starting from her 66th birthday to 88th birthday:

1. Withdrawing $200,000 from her account on her 65th birthday for a 3-month trip in celebration of her retirement.

2. Withdrawing $100,000 from her account on her 70th birthday and another $100,000 on her 80th birthday for organizing luxury birthday parties for herself.

3. Donating $80,000 every year to her university, starting from her 80th birthday to 88th birthday.

Assume that Connie will make her first deposit six months from today and the last deposit one month before her retirement.

In order to fulfill her retirement plan, how much money must Connie have in her savings account on her 65th birthday when she retires?

(ii) What should her monthly deposit be in order to fulfill her retirement plan?

Answer 1

	(a)	INSURANCE COMPANY A
		Number of annual withdrawal	23	(88-65)
		Amount of annual withdrawal	$300,000
		Imterest rate	10%
		Present Value of annual withdrawal on 65th Birthday	$2,664,966	(Using PV function with Rate=10%,Nper=23, Pmt=-300000)
		Number of instalments of savings	31	(65-34)
		Imterest rate	10%
		Future value required at the end of 31 years	$14,647.22	(Using PMT function with Rate=10%,Nper=31, FV=-2664966)
		She need to deposit every year	$14,647.22
	(b)	INSURANCE COMPANY B
		Present Value (PV) of Cash flow=(Cash flow)/(1+i)^N
		i= interest rate=6%=0.06, N=Year of cash flow
			N	A	B=A/(1.06^N)
			Years after	Withdrawal	PV at retirement
			Retirement	Amount	of withdrawal amount
		1. 65th Birthday	0	$200,000	$                     200,000.00
		70th birthday for birthday party	5	$100,000	$                       74,725.82
		80th birthday for birthday party	15	$100,000	$                       41,726.51
		80th birthday for donation	15	$80,000	$                       33,381.20
		81st birthday for donation	16	$80,000	$                       31,491.70
		82nd birthday for donation	17	$80,000	$                       29,709.15
		83rd birthday for donation	18	$80,000	$                       28,027.50
		84th birthday for donation	19	$80,000	$                       26,441.04
		85th birthday for donation	20	$80,000	$                       24,944.38
		86th birthday for donation	21	$80,000	$                       23,532.43
		87th birthday for donation	22	$80,000	$                       22,200.41
		88th birthday for donation	23	$80,000	$                       20,943.78
				SUM	$                     557,123.93
		Amount of money Connie should have in savings account	$   557,123.93
		Number of monthly deposits to be made	378	(31*12+6)
		Monthly Interest Rate=r
		EAR=15%=0.15
		(1+r)^12=1.15
		1+r=1.15^(1/12)=	1.011714917
		r=0.0117
		Monthly Deposit Required	$6,599.63	(Using PMT function with Rate=0.0117,Nper=378, FV=-557123.93)