Question

It is estimated that you will pay about ​$80 comma 00080,000 into the social security system​ (FICA) over your 4040​-year work span. For​ simplicity, assume this is an annuity of ​$2 comma 0002,000 per​ year, starting a year from today with your 2626th birthday and continuing through your 6565th birthday​ (your last annual contribution is on your 6565th ​birthday) . a. What is the future equivalent worth of your social security savings when you retire at age 6565 if the​ government's interest rate is 88​% per​ year? b. What annual withdrawal can you make if you expect to live 2525 years in​ retirement? Let i​ =88​% per year.

Answer 1

Part a: The Future value of the annuity after 40 years is $518113.24.

Part b: The per year withdrawal in retirement for 25 years will be $48536.19.

Explanation:

As the numbers are appearing as a duplication taking all these values as single.

Part a

Future value is given as

`FV=PMT * [\frac{{(1+I)}^(N)-1}{I}]`

Here

• PMT is the annual value which is $2000 per year
• I is the interest rate which is given as 8%
• N is 40

`FV=PMT * [\frac{{(1+I)}^(N)-1}{I}]\\\\FV=2000 * [\frac{({1+.08})^(40)-1}{.08}]\\FV=\$ 518113.03`

So the Future value of the annuity after 40 years is $518113.24.

Part b

Per year withdrawal is given as

`PY=(Value)/((1 - (1)/((1+I)^N))/(I))`

Here

• PY is the per year withdrawal
• Value is the total amount which is $ 518113 as calculated in part a
• I is the rate of interest which is 8%
• N is 25 years as expected life to live in retirement.

So the value is given as

`PY=(Value)/((1 - (1)/((1+I)^N))/(I))\\PY=(518113)/((1 - (1)/((1+0.08)^(25)))/(0.08))\\PY=(518113)/(10.6747)\\PY=\$ 48536.19`

So the per year withdrawal in retirement for 25 years will be $48536.