Answer:
Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires.
Step-by-step explanation:
Given monthly income of Ron is $3,142.23
Ron contributes 10% of his monthly income that is $ 314.223
Given : Ron is 25 years old and is retiring at the age of 65. so he has 40 years to contribute.
Total amount he contribute in 40 years paying 5.5% compounded monthly is given by
interest rate(r) =[tex]\frac{0.055}{12}[/tex]
time period = 40 years = 480 months
Principal amount = $ 314.223
Future value = [tex]P(\frac{(1+r)^n-1}{r} )[/tex]
Substitute , we get,
[tex]=3142.23\cdot\frac{.10\left(\left(1+\frac{.055}{12}\right)^{12\cdot40}-1\right)}{\frac{0.055}{12}}[/tex]
Thus, future value is $547074.681009.
After retirement his monthly income when he has $547074.681009 amount.
[tex]P=\dfrac{A\cdot\frac{i}{12} }{1-(1+\frac{i}{12})^{-n}}[/tex]
Putting values , we get,
[tex]P=\frac{\left(547074.68\cdot\frac{.055}{12}\right)}{1-\left(1+\frac{0.055}{12}\right)^{-240}}[/tex]
P = $3763.25
He will receive a monthly income of $3763.25.
But given he will need a monthly income of $4,123 for 20 years which is not met by Ron.
So,the amount he need to supplement his monthly income when he retires by (4123-3763.25)= $359.74
Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires.
