Mathematics, 29.07.2019 04:00 psychocatgirl1

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

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Answer from: shainaanderson24

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

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

$n=30\times12=360$

Now, put all the values we get,

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

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

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

$D=\frac{1-0.21723}{0.00425}$

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

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

Therefore, Option A is correct.

The amount needed is $396721.78.

Answer from: esta54

The amount needed at the time of retirement is $\boxed{\$ 396721.78}$ .Option (a) is correct.

Further explanation:

The present value formula can be expressed as follows,

$\boxed{{\text{PV}} = A \times \frac{{\left[ {1 - {{\left( {1 + \frac{i}{n}} \right)}^{ - n}}} \right]}}{{\frac{i}{n}}}}$

Here, $\text{A}$ represents the amount, $\text{PV}$ represents the present value, $\text{i}$ represent the interest rate and $\text{n}$ represents the time.

Given:

The payments can be made for 30 years.

The number of months are $360{\text{ months}}.$

The account pay interest rate is $i = 5.1\%$ compounded monthly.

The withdraws amount is $\$ 450.$

Explanation:

The value of $\text{n}$ is 360.

The value of $\text{i}$ is $5.1\%.$

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

$\begin{aligned}{\text{PV}}&= {\text{A}} \times \dfrac{{\left[ {1 - {{\left( {1 + \dfrac{i}{{12}}} \right)}^{ - 360}}} \right]}}{{\dfrac{i}{{12}}}}\\&= 2154 \times \dfrac{{\left[ {1 - {{\left( {1 + \dfrac{{0.051}}{{12}}} \right)}^{ - 360}}} \right]}}{{\dfrac{{0.051}}{{12}}}}\\&= 2154 \times \dfrac{{\left[ {1 - 0.21724} \right]}}{{0.00425}}\\\end{aligned}$

Further solve the above equation.

$\begin{aligned}{\text{PV}}&= 2154 \times \frac{{0.78276}}{{0.00425}}\\&= 2154 \times 184.20\\&= \$ 396721.78\\\end{aligned}$

The amount needed at the time of retirement is $\boxed{\$ 396721.78}$ . Option (a) is correct.

Learn more:

Learn more about inverse of the Learn more about equation of circle Learn more about range and domain of the function

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.

Answer from: Quest

you first to choose the points and then move from then as the slope you have

Answer from: Quest

Ithink the answer will be 5

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