Your job pays you only once a year for all the work you did over the previous 12 months. Today,

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 $67,000 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 10.7 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? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

 

Future value

$

Explanation:

Since your salary grows at 4 percent per year, your salary next year will be:

 

Next year’s salary = $67,000 (1 + 0.040)

Next year’s salary = $69,680

This means your deposit next year will be:

Next year’s deposit = $69,680(0.10)

Next year’s deposit = $6,968

Since your salary grows at 4 percent, your deposit will also grow at 4 percent. We can use the present value of a growing perpetuity equation to find the value of your deposits today. Doing so, we find:

PV = C {[1/(r – g)] – [1/(r – g)] × [(1 + g)/(1 + r)]t}

PV = $6,968{[1/(0.107 – 0.040)] – [1/(0.107 – 0.040)] × [(1 + 0.040)/(1 + 0.107)]45}

PV = $97,735.44

Now, we can find the future value of this lump sum in 45 years. We find:

FV = PV(1 + r)t

FV = $97,735.44(1 + 0.11)45

FV = $9,477,526.47

This is the value of your savings in 45 years.