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

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

Discount factor $D=\frac{1-(1+i)^{-n}}{i}$  

Where, Amount = ?

Monthly payment = $1205.78

Rate r= 5.5%=0.055  

$i=\frac{0.055}{12}=0.004583$  

Time = 5 years  

$n=5\times12=60$  

Now, put all the values we get,  

$D=\frac{1-(1+i)^{-n}}{i}$  

$D=\frac{1-(1+0.004583)^{-60}}{0.004583}$  

$D=\frac{1-(1.004583)^{-60}}{0.004583}$ 

$D=\frac{1-0.7600}{0.004583}$  

$D=\frac{0.2399}{0.004583}$  

$D=52.35$  

Substitute the value in the formula,

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

$1205.78=\frac{A}{52.35}$  

$A=1205.78\times 52.35$  

$A=63126.00$  

Therefore, Option d is correct.

The amount needed in the account is $63,126.00

Answer 2

d.$63,126.00 I think haha