Question

You are 47 years old today and want to plan for retirement at age 65. You want to set aside an equal amount every year from now to retirement. You expect to live to age 87 and want to withdraw a fixed amount each year during retirement that at age 65 will have the same purchasing power as $73,868 has today. You plan on withdrawing the money starting the day you retire. You have not saved any money for retirement. Inflation is assumed to be 4.0% in the future. You expect to earn an 8.5% return on your investments in the future. How much do you need to save each year until retirement to meet your goal?

Answer 1

First, we find out how much money we need to have at retirement to satisfy the assumed conditions.

Here, we find the annual requirement considering the inflation factor

Annual requirement = $73,868*(1.04^(Age-47))

Total value required at year 65 = Value of all the future cash-flows discounted at 8.5%

Total Value required at year 65	$2,070,160.35
Age	Annual requirement
65	149643.0144
66	155628.7349
67	161853.8843
68	168328.0397
69	175061.1613
70	182063.6077
71	189346.1521
72	196919.9981
73	204796.7981
74	212988.67
75	221508.2168
76	230368.5455
77	239583.2873
78	249166.6188
79	259133.2835
80	269498.6149
81	280278.5594
82	291489.7018
83	303149.2899
84	315275.2615
85	327886.272
86	341001.7228
87	354641.7917

Now, we have the future value required after 18 years (65-47) = $2070160.35

This is the future value at age 65 of the annual savings

We need to find annual installment to achieve this FV

We use PMT function in excel

PV = .0

FV = 2070160.35

N = 18

I/Y = 0.085

We get PMT = $52645.03

Hence, $52645.03 is the amount you need to save each year until retirement to meet your goal