Question

Suppose that your retirement benefits during your first year of retirement are $60,000 per year which is just enough to meet your cost of living during the first year. However, your cost of living is expected to increase at an annual rate of 5% due to inflation. If there is no cost-of-living adjustment in your retirement pension, then some of your future living cost has to come from savings other than retirement pension. If your saving account earns 7% interest a year, how much should you set aside in order to meet this future increase in the cost of living for 25 years

Answer 1

The money side aside in order to meet this future increase in the cost of living for 25 years is $429,060

Step-by-step explanation:

Solution

Given that:

The first year retirement benefit is = $60,000

Expected increase of cost of living at an annual rate = 5%

Savings earn account = 7%

Now,

We find the the pension current worth

P₁ = $60,000 (P/A, i, n)

= $60,000 (P/A 7%, 25)

$60,000 (11.654)

= 699, 254

Thus,

we compute the current worth of cost of living by applying the factor of geometric series.

P₂ = $60,000 (P/A, g,i, n)

= $60,000 (P/A, 5% 7%, 25)

= $60,000 [ 1-(1+0.05)^25 + (1+0.07)^-25/0.07 -0.05]

= $60,000 (1 - 0.6239/0.02)

=$60,000 (0.3761/0.02)

= $22,566/0.02 =$1,128,300

Now, we calculate the money that will be saved

Which is $1,128,300 - $699,254

= $429,060