Answer:
FV = 2,621,048.23
Explanation:
we will calcualte the future value of an annuity with an geometric progression:
[tex]\frac{(1+r)^{n} -(1+q)^{n}}{r - q} = FV[/tex]
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)
[tex]\frac{(1+0.092)^{39} -(1+0.03)^{39}}{0.092 - 0.03} = FV[/tex]
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:
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
