Question

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 1

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

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

Where,

Amount = ?

Monthly payment  M=$2154

Rate r= 5.1%=0.051

$i=\frac{0.05}{12}=0.00425$

Time = 30 years  

$n=30\times12=360$

Substitute all the values,

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

$D=\frac{1-(1+0.00425)^{-360}}{0.00425}$

$D=\frac{1-(1.00425)^{-360}}{0.00425}$

$D=\frac{1-0.21723}{0.00425}$  

$D=\frac{0.78277}{0.00425}$

$D=\ 184.1811$

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

$2154=\frac{A}{184.1811}$

$A=2154\times 184.1811$  

$A=\ 396721.778$

Nearest cent, $A=\ 396721.78$

Therefore, the amount needed such that when it comes time for retirement is $396721.78.