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Tyler wants to have $250,000 in his retirement account by the time he retires in 30 years. The interest rate is 5%. Use the annuity formula to calculate the amount Tyler needs to deposit on a monthly basis in order to reach his goal. When solving, round numbers to the nearest hundred-thousandth. Round your final answer to the nearest cent.

Respuesta :

Using the monthly payment formula, he needs to deposit A = $1,342.12 a month to reach his goal.

What is the monthly payment formula?

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

  • P is the initial amount.
  • r is the interest rate.
  • n is the number of payments.

For this problem, the parameters are:

P = 250000, r = 0.05, n = 12 x 30 = 360.

Then:

r/12 = 0.05/12 = 0.004167.

Then:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 250000\frac{0.004167(1+0.004167)^{360}}{(1+0.004167)^{360} - 1}[/tex]

A = $1,342.12

More can be learned about the monthly payment formula at https://brainly.com/question/26267630

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