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How much would $500 invested at 6% interest compounded monthly be worth after 5 years? Round your answer to the nearest cent. A(t)=P(1+r/n)^nt

Respuesta :

Answer:

$674.42.

Step-by-step explanation:

Givens

  • The principal of the investment is $500.
  • The interest rate compounded monthly is %6 or 0.06.
  • The time invested is 5 years.

To solve these type of problems, we need to recur to Interest Compound Formula, which is

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

Where [tex]A[/tex] is the total amount of money after the time compounded, [tex]P[/tex] is the principal, [tex]r[/tex] is the interest rate, [tex]n[/tex] is the number of compounded periods in one year and [tex]r[/tex] is time in years.

So,

[tex]P=500\\r=0.06\\n=12\\t=5[/tex]

If the problem states that the interest is compounded monthly, then there are gonna be 12 compounded periods in one year. Replacing all these values, we have

[tex]A(t)=P(1+\frac{r}{n} )^{nt}\\A(t)=500(1+\frac{0.06}{12} )^{12(5)}\\ A(t)=500(1.005)^{60}= 674.42[/tex]

Therefore, the total amount of money after 5 years is $674.42.

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