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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.

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danialamin

Answer:

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.

Step-by-step explanation:

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

Part a

Future value is given as

[tex]FV=PMT \times [\frac{{(1+I)}^{N}-1}{I}][/tex]

Here

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

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

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

Part b

Per year withdrawal is given as

[tex]PY=\frac{Value}{\frac{1 - \frac{1}{(1+I)^N}}{I}}[/tex]

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

[tex]PY=\frac{Value}{\frac{1 - \frac{1}{(1+I)^N}}{I}}\\PY=\frac{518113}{\frac{1 - \frac{1}{(1+0.08)^{25}}}{0.08}}\\PY=\frac{518113}{10.6747}\\PY=\$ 48536.19[/tex]

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

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