In: Finance
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?
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 |