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Carla deposited $8500 into an account paying 7.9% annual interest compounded monthly. How much
money will be in the account after 6 years? (also called Future value).
Round to the nearest cent if necessary.

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shashichoubey081

Answer:

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$13,633.26 will be in the account after 6 years.

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This question is solved using the compound interest formula.

Compound interest:

The compound interest formula is given by:

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

Where 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 and t is the time in years for which the money is invested or borrowed.

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In this question:

  • Deposit of $8500 means that [tex]P = 8500[/tex].
  • Interest rate of 7.9% means that [rex]r = 0.079[/tex].
  • Compounded monthly, that is, 12 times an year, so [tex]n = 12[/tex].
  • 6 years, thus, [tex]t = 6[/tex].

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How much  money will be in the account after 6 years?

This is A(6), so:

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

[tex]A(6) = 8500(1 + \frac{0.079}{12})^{12\times6}[/tex]

[tex]A(6) = 13,633.26[/tex]

$13,633.26 will be in the account after 6 years.

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