Determine the amount needed such that when it comes time for retirement, an individual can make monthly withdraws in the amount of $2,154 for 30 years from an account paying 5.1% compounded monthly. Round your answer to the nearest cent.

Answer:The amount needed such that when it comes time for retirement is $396721.78.Step-by-step explanation:Given : An individual can make monthly withdraws in the amount of $2,154 for 30 years from an account paying 5.1% compounded monthly.To find : The amount needed such that when it comes time for retirement?Solution :Using the formula of monthly payment,Monthly payment, [tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex] Discount factor D=\frac{1-(1+i)^{-n}}{i}  Where, Amount = ?Monthly payment  M=$2154 Rate r= 5.1%=0.051 [tex]i=\frac{0.05}{12}=0.00425[/tex] Time = 30 years   [tex]n=30\times12=360[/tex] Substitute all the values,[tex]D=\frac{1-(1+i)^{-n}}{i}[/tex][tex]D=\frac{1-(1+0.00425)^{-360}}{0.00425}[/tex] [tex]D=\frac{1-(1.00425)^{-360}}{0.00425}[/tex] [tex]D=\frac{1-0.21723}{0.00425}[/tex]   [tex]D=\frac{0.78277}{0.00425}[/tex][tex]D=\$184.1811[/tex] Monthly payment, [tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex][tex]2154=\frac{A}{184.1811}[/tex] [tex]A=2154\times 184.1811[/tex]   [tex]A=\$396721.778[/tex] Nearest cent, [tex]A=\$396721.78[/tex]Therefore, the amount needed such that when it comes time for retirement is $396721.78.