Your 68 year old mother plans to retire in 2 yars and she expects to live indepe

Question

Your 68 year old mother plans to retire in 2 yars and she expects to live independently for 3 years. She wants a retirement income that has, in the first year the same purchasing power as 60,000 has today. However her retirement income will be of a fixed amount so her real income will decline over time. Her retirement income will start the day she retires ( 2 years from today), and she will receive a totla of 3 retirements payments. In flation is expected to be constant at 6%. Your mother has $100000 in savings now an she can earn 9% on savings now and in the future. How much must shes save each year starting today to meet her retirement goals?

Explanation / Answer

Step 1

Value of Current Purchasing Power of 60,000, after 2 years

=60000*(1+0.06)^2 = $ 67,416

Step 2

Year

Cash Flow

PV

0

$ 67,416

=$ 67,416/(1+0.06)^0 = $ 67,416

1

$ 67,416

=$ 67,416/(1+0.06)^1 = $ 63,600

2

$ 67,416

=$ 67,416/(1+0.06)^2 = $ 60,000

Present Value

=1,91,016

Investment required at the end of Year Two is $ 1, 91,016.

Step 3

Existing Investment will worth 100,000(1+.09)^2 = $118,810.

So Amount to Be Saved in two years equals to (1, 91,016. - $118,810.) = 72,206.

Step 4

= (72206*0.06)/((1.06)^2-1) = 35,051.45.

Assumption

Step 1

Value of Current Purchasing Power of 60,000, after 2 years

=60000*(1+0.06)^2 = $ 67,416

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