Answer:
Option d - $63,126.00
Step-by-step explanation:
Given : You would like to withdraw a monthly salary of $1,205.78 from an account paying 5.5% interest, compounded monthly.
To find : Determine the amount needed in the account such that you can withdraw the needed amount at the end of each month for 5 years?
Solution :
Applying formula of monthly payment ,
Monthly payment, [tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex]
Discount factor [tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]
Where, Amount = ?
Monthly payment = $1205.78
Rate r= 5.5%=0.055
[tex]i=\frac{0.055}{12}=0.004583[/tex]
Time = 5 years
[tex]n=5\times12=60[/tex]
Now, put all the values we get,
[tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]
[tex]D=\frac{1-(1+0.004583)^{-60}}{0.004583}[/tex]
[tex]D=\frac{1-(1.004583)^{-60}}{0.004583}[/tex]
[tex]D=\frac{1-0.7600}{0.004583}[/tex]
[tex]D=\frac{0.2399}{0.004583}[/tex]
[tex]D=52.35[/tex]
Substitute the value in the formula,
[tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex]
[tex]1205.78=\frac{A}{52.35}[/tex]
[tex]A=1205.78\times 52.35[/tex]
[tex]A=63126.00[/tex]
Therefore, Option d is correct.
The amount needed in the account is $63,126.00
