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Welcome to the article You want to have tex 313 000 00 tex when you retire in 30 years for an annuity How much money should be deposited at. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!

You want to have [tex]$313,000.00[/tex] when you retire in 30 years for an annuity. How much money should be deposited at the end of each month in an investment plan that pays 4.4% compounded monthly, so you will have [tex]$313,000.00[/tex] in 30 years?

(Round to 2 decimal places.)

Answer :

The monthly payment amounts to approximately $467.27 (rounded to two decimal places).

The formula is as follows:

[tex]FV = P \times \frac{(1 + r)^n - 1}{r}[/tex]

Where:

  • [tex]FV[/tex] is the future value of the annuity (which is $313,000).
  • [tex]P[/tex] is the monthly payment you want to calculate.
  • [tex]r[/tex] is the monthly interest rate (annual rate divided by 12).
  • [tex]n[/tex] is the total number of payments (number of years multiplied by 12).

Step 1: Determine the monthly interest rate

Given the annual interest rate is 4.4%, we calculate the monthly interest rate as follows:

[tex]r = \frac{4.4\%}{12} = 0.0044/12 \approx 0.00366667[/tex]

Step 2: Determine the total number of payments

Since the investment period is 30 years, the total number of monthly payments will be:

[tex]n = 30 \times 12 = 360[/tex]

Step 3: Substitute the values into the future value formula

We can rearrange the formula to solve for monthly payment [tex]P[/tex]:

[tex]P = \frac{FV \cdot r}{(1 + r)^n - 1}[/tex]

Substituting the known values:

[tex]P = \frac{313,000 \cdot 0.00366667}{(1 + 0.00366667)^{360} - 1}[/tex]

Step 4: Calculate [tex](1 + r)^n[/tex]

First, let's calculate [tex](1 + r)^{360}[/tex]:

[tex](1 + 0.00366667)^{360} \approx 3.452445[/tex]

Step 5: Substitute this back to find [tex]P[/tex]:

[tex]P = \frac{313,000 \cdot 0.00366667}{3.452445 - 1}[/tex]

Calculating the denominator:
[tex]3.452445 - 1 \approx 2.452445[/tex]

Now substituting back:

[tex]P \approx \frac{313,000 \cdot 0.00366667}{2.452445} \approx \frac{1,147.64}{2.452445} \approx 467.27[/tex]

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Rewritten by : Brahmana