Your job pays you only once a year, for all the work you did over the previous 12 months. Today, December 31, you just received your salary of $70,000 and you plan to spend all of it. However, you want to start saving for retirement beginning next year. You have decided that one year from today you will begin depositing 8 percent of your annual salary in an account that will earn 11 percent per year. Your salary will increase at 4 percent per year throughout your career. How much money will you have on the date of your retirement 45 years from today?

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TomShelby TomShelby · Answer 1 · 2019-10-05T03:08:02+02:00

Answer:

In 45 years we are going to have: 1,461,731.021

Explanation:

we are going to deposit the 8% of each salary.

we must notice the amount will grow by 4% each time. this will be a geometric annuity as the quota increase as a reason of 1 + q

the formula is:

[tex]\frac{1-(1+g)^{n}\times (1+r)^{-n} }{r - g}[/tex]

grow = q = 0.04

capital return = 0.11

First quota = we will deposit 8% of the next year salary:

70,000 x 1.04 x 8% = 5,824

n= we retire in 45 year but we start doing this deposit next year= 44

1,461,731.021