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Cooper is opening an online savings account to hold his $19,000 emergency fund. The online account pays 1.6 interest compounded monthly. If Cooper does not deposit or withdraw any money from the account, how much will be in the account in 5 years ?

Sagot :

Using compound interest, it is found that $20,581.36 will be in the account in 5 years.

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:

  • The initial deposit is of P = 19000.
  • The rate is of r = 0.016.
  • Monthly compounding, hence n = 12.
  • 5 years, hence t = 5.

Then:

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

[tex]A(5) = 19000\left(1 + \frac{0.016}{12}\right)^{12(5)}[/tex]

[tex]A(5) = 20581.36[/tex]

$20,581.36 will be in the account in 5 years.

You can learn more about compound interest at https://brainly.com/question/25781328