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. a. $396,721.78 b. $398,407.85 c. $775,440 d. $1,833,962.40

Option A - $396,721.78

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 :

We apply the formula of monthly payment,

Monthly payment,  

Discount factor  

Where, Amount = ?

Monthly payment  M=$2154

Rate r= 5.1%=0.051

Time = 30 years  

Now, put all the values we get,  

Monthly payment,  

Therefore, Option A is correct.      

The amount needed is $396721.78.

The amount needed at the time of retirement is .Option (a) is correct.

Further explanation:

The present value formula can be expressed as follows,

Here, represents the amount, represents the present value, represent the interest rate and represents the time.

Given:

The payments can be made for 30 years.

The number of months are

The account pay interest rate is compounded monthly.

The withdraws amount is

Explanation:

The value of is 360.

The value of is

The present value or the amount needed at the time of retirement can be obtained as follows,

Further solve the above equation.

The amount needed at the time of retirement is . Option (a) is correct.

Learn more:

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Loan Schedule

Keywords: amount, needed, retirement, individual, time of retirement, withdraws, account, paying, 5.1% compounded monthly, nearest cents, monthly, interest rate.

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step-by-step explanation:

the first option is the answer.