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You would like to have $20,000 to use a down payment for a home in five years by making regular, end-of-month deposits in an annuity that pays 6% interest compounded monthly. How much of the $20,000 down payment comes from interest earned? Round your answer to the nearest cent. Do NOT round until you have calculated the final answer. Do NOT include the dollar sign in the answer box below.

Respuesta :

Using compound interest, it is found that $5,172.56 comes from interest earned

What is compound interest?

The amount of money earned, in compound interest, after t years, is given by:

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

In which:

  • A(t) is the amount of money after t years.
  • P is the principal(the initial sum of money).
  • r is the interest rate(as a decimal value).
  • n is the number of times that interest is compounded per year.
  • t is the time in years for which the money is invested or borrowed.

In this problem:

  • $20,000 is required in five years, hence t = 5, A(5) = 20000.
  • Interest rate of 6%, hence r = 0.06.
  • Monthly compounding, hence n = 12.

First, we have to find the principal needed, hence:

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

[tex]20000 = P\left(1 + \frac{0.06}{12}\right)^{12(5)}[/tex]

[tex]P = \frac{20000}{(1.005)^{60}}[/tex]

[tex]P = 14827.44[/tex]

Hence:

  • $14,827.44 comes from the principal.
  • $5,172.56 comes from interest earned, as $20,000 - $14,827.44 = $5,172.56.

To learn more about compound interest, you can take a look at https://brainly.com/question/25781328

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