Question

You plan on supplementing your income. You would like to withdraw a monthly salary of $1,205.78 from an account paying 5.5% interest, compounded monthly. Determine the amount needed in the account such that you can withdraw the needed amount at the end of each month for 5 years. Round to the nearest cent.

a. $83,055.12
b. $63,415.33
c. $72,346.00
d. $63,126.00

Answer 1

d.$63,126.00 I think haha

Answer 2

Option d - $63,126.00

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,
`M=\frac{\text{Amount}}{\text{Discount factor}}`

Discount factor
`D=(1-(1+i)^(-n))/(i)`

Where, Amount = ?

Monthly payment = $1205.78

Rate r= 5.5%=0.055

`i=(0.055)/(12)=0.004583`

Time = 5 years

`n=5*12=60`

Now, put all the values we get,

`D=(1-(1+i)^(-n))/(i)`

`D=(1-(1+0.004583)^(-60))/(0.004583)`

`D=(1-(1.004583)^(-60))/(0.004583)`

`D=(1-0.7600)/(0.004583)`

`D=(0.2399)/(0.004583)`

`D=52.35`

Substitute the value in the formula,

`M=\frac{\text{Amount}}{\text{Discount factor}}`

`1205.78=(A)/(52.35)`

`A=1205.78* 52.35`

`A=63126.00`

Therefore, Option d is correct.

The amount needed in the account is $63,126.00