Question

Your job pays you only once a year for all the work you did over the previous 12 months. Today, December 31, you received your salary of $52,000 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 9.2 percent per year. Your salary will increase at 3 percent per year throughout your career. How much money will you have on the date of your retirement 40 years from today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

FV =  2,621,048.23

Explanation:

we will calcualte the future value of an annuity with an geometric progression:

$\frac{(1+r)^{n} -(1+q)^{n}}{r - q} = FV$

g 0.03

r 0.092

C 5,356 ( we will save next year (52,000 x 1.03) the 10% )

n 39 (we start saving next year)

$\frac{(1+0.092)^{39} -(1+0.03)^{39}}{0.092 - 0.03} = FV$

FV = 2,400,227.319

As we deposit at the first day of the year this will be an annuity-due so we will multiply by (1 +r)

FV =  2,621,048.23

Answer 2

Answer:

the answer is $2 830 830. 09

Explanation:

The first thing to calculate is the growth of salary o fwhich it grows by 3%

$52000*1.03=53560

The for the first year of saving we calculate the portion to be saved

53560*0.1= 5356

in order to find the future value of savings we will use the pv of perpetuity to find the value of the deposit today

PV = C{(1/(r-g)) - (1/(r-g)*(1+g)/(1+r)^t}

     =5356*{(1/0.092-0.03) - (1/(0.092-0.03)*(1.03)/(1.092)^40}

     =83754.52289

Then from the PV we can calculate the future value as

FV = 83754.52289 *(1.092)^40

      =2 830 830 .09