Bob is 37 years old and is an account manager with a large telecom company. He’s...

Bob is 37 years old and is an account manager with a large telecom company. He’s been dragging his feet with his retirement plan, opting instead for expensive trips to Vegas and Aspen. He’s decided it’s time to get serious about saving for his retirement. He plans to retire at age 67 and travel the world. Because of this plan, he figures he needs approximately $70,000/year in retirement. His grandfather lived until he was 86 and his dad is in perfect health at age 70, therefore Bob figures he should plan to be around until he’s 90. So far, he has $11,000 saved for retirement and because of his aggressive investment philosophy, is planning for a return on all his investments before retirement of 8%. Following retirement he will invest more conservatively and will plan for a 5% return on investments. His company’s retirement plan is defined contribution, so he doesn’t plan on getting a pension. He is not counting on social security to be around, so he isn’t including that in his plan. Thus, his entire retirement will be funded on his own savings.

2) How much money will Bob need during retirement based on his calculations?

3) How much will Bob need to save each year to be ready for retirement at age 67?

Expert Solution

Bob need $ 70000 per year for 23 years (90 - 67) after his retirement for travel
He will earn 5% return on his investment after his retirement
we will use 5% PV factor for deriving Investment value at the time of retirement
Below is the gross amount required at the time of retirement value he needed to get $ 70000 per year after his retirement

n	I = 0.05	Retuns per year	Value of investment at the time of retirement
1	0.952380952	$ 70,000.00	$ 66,666.67
2	0.907029478	$ 70,000.00	$ 63,492.06
3	0.863837599	$ 70,000.00	$ 60,468.63
4	0.822702475	$ 70,000.00	$ 57,589.17
5	0.783526166	$ 70,000.00	$ 54,846.83
6	0.746215397	$ 70,000.00	$ 52,235.08
7	0.71068133	$ 70,000.00	$ 49,747.69
8	0.676839362	$ 70,000.00	$ 47,378.76
9	0.644608916	$ 70,000.00	$ 45,122.62
10	0.613913254	$ 70,000.00	$ 42,973.93
11	0.584679289	$ 70,000.00	$ 40,927.55
12	0.556837418	$ 70,000.00	$ 38,978.62
13	0.530321351	$ 70,000.00	$ 37,122.49
14	0.505067953	$ 70,000.00	$ 35,354.76
15	0.481017098	$ 70,000.00	$ 33,671.20
16	0.458111522	$ 70,000.00	$ 32,067.81
17	0.436296688	$ 70,000.00	$ 30,540.77
18	0.415520655	$ 70,000.00	$ 29,086.45
19	0.395733957	$ 70,000.00	$ 27,701.38
20	0.376889483	$ 70,000.00	$ 26,382.26
21	0.358942365	$ 70,000.00	$ 25,125.97
22	0.341849871	$ 70,000.00	$ 23,929.49
23	0.325571306	$ 70,000.00	$ 22,789.99
Total amount required at retirement			$ 9,44,200.17

Bob already have $ 11000 savings for retirement which will grow at 8% for 30 years i.e. till his retirement

i.e.	= $ 11,000.00 x annuity for n=30, i=8%
=	$ 1,10,689.23

Net amount required at the time of retirement will be
=	944,200.171884504 - 110,689.225779807
=	$ 8,33,510.95

He will earn 8% return on his investment till his retirement
Calculation of amount that need to be invest per year till retirement by bob

Invesment amount =		Amount required at the time of retirement
		Cumulative annuity factor for i= 8%, n= 30
	=	$ 8,33,510.95
		122.3520854	(see note for annuity factor)
	=	$ 6,812.40

A ) Bob need $ 944,200.17 at the time of retirement based on his calculations

B ) Bob need to save $ 6,812.40 each year to get ready fo retirement

Note :
30 years of investment (i.e. age of retirement less current age)

FUTURE VALUE OF $1
n	0.08
1	1.086217443
2	1.1664
3	1.259712
4	1.36048896
5	1.469328077
6	1.586874323
7	1.713824269
8	1.85093021
9	1.999004627
10	2.158924997
11	2.331638997
12	2.518170117
13	2.719623726
14	2.937193624
15	3.172169114
16	3.425942643
17	3.700018055
18	3.996019499
19	4.315701059
20	4.660957144
21	5.033833715
22	5.436540413
23	5.871463646
24	6.341180737
25	6.848475196
26	7.396353212
27	7.988061469
28	8.627106386
29	9.317274897
30	10.06265689
Cumulative annuity factor	122.4320854

jeff jeffy answered 2 years ago

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