nourmaali

27.02.2021 •

Mathematics

Ere by the warme retation if given domain is 1 and 2 2012 and
which of the following is a relation

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Ответ:

ddvinks6825

11.06.2021

Mathematics

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.

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Ere by the warme retation if given domain is 1 and 2 2012 andwhich of the following is a relation​