You have 34 years left until retirement and want to retire with $3.6 million. Your salary is paid

You have 34 years left until retirement and want to retire with $3.6 million. Your salary is paid annually, and you will receive $52,000 at the end of the current year. Your salary will increase at 2.2 percent per year, and you can earn a 15.2 percent return on the money you invest. If you save a constant percentage of your salary, what percentage of your salary must you save each year? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

 

Percent of salary to save

%

Explanation:

We need to find the lump sum payment into the retirement account. The present value of the desired amount at retirement is:

   

PV = FV/(1 + r)t

PV = $3,600,000/(1 + 0.152)34

PV = $29,303.41

    

This is the value today. Since the savings are in the form of a growing annuity, we can use the growing annuity equation and solve for the payment. Doing so, we get:

   

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

$29,303.41 = C{[1 – ((1 + 0.022)/(1 + 0.152))34 ] / (0.152 – 0.022)}

C = $3,875.56

  

This is the amount you need to save next year. So, the percentage of your salary is:

  

Percentage of salary = $3,875.56/$52,000

Percentage of salary = 0.0745, or 7.45%

 

Note that this is the percentage of your salary you must save each year. Since your salary is increasing at 2.2 percent, and the savings are increasing at 2.2 percent, the percentage of salary will remain constant.