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 $54,000 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 10 percent of your annual salary in an account that will earn 9.4 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

I will have $5,319,216.16 on the date of retiremnet.

Explanation:

First, we need to calculate the amount of deposit

Amount of annual deposit = Annual salary x Deposit rate

Amount of annual deposit = $54,000 x 10%

Amount of annual deposit = $5,400

Now use the following formula to calculate the balance in the account after 45 years from today

Future value of annuity = [ Periodic Annuity payment x ( 1 + growth rate ) / ( Interst rate - growth rate ) ] x [ ( 1 + interest rate )^numbers ofyears - ( 1 + growth rate )^numbers of years ]

Where

Periodic Annuity payment = Amount of annual deposit = $5,400

Periodic interest rate = 9.4%

Periodic growth rate = 4%

Numbers of years = 45 years

Future value of annuity = Balance after 45 years = ?

Placing values in the formula

Balance after 45 years = [ $5,400 x ( 1 + 4% ) / ( 9.4% - 4% ) ] x [ ( 1 + 9.4% )^45 - ( 1 + 4% )^45 ]

Balance after 45 years = [ $5,616 / 5.4% ] x [ ( 1.094^45 ) - ( 1.04^45) ]

Balance after 45 years =  $104,000 x [ 56.987484867 - 5.841175681  ]

Balance after 45 years =  $104,000 x 51.146309186

Balance after 45 years =  $5,319,216.155344

Balance after 45 years =  $5,319,216.16

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