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))
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.