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James wants to have earned $7,592 amount of interest in 16 years. Currently he finds that hisannual interest rate is 9.04%. Calculate how much money James needs to invest as his principal inorder to achieve this goal.Round answers to the nearest hundredth (two decimal places) of a year.

Respuesta :

We know that

• The earnings are $7,592.

,

• The time is 16 years.

,

• The annual interest rate is 9.04%.

This problem is about simple interest, its formula is

[tex]A=P(1+rt)[/tex]

Where A = 7,592, r = 9.04, t = 16, and P is the principal.

Let's replace each value.

[tex]7,592=P(1+0.0904(16))[/tex]

Notice that 9.04% is equivalent to 0.0904.

Now, we solve it for P.

[tex]\begin{gathered} 7,592=P(1+1.4464) \\ 7,592=P(2.4464) \\ P=\frac{7,592}{2.4464} \\ P\approx3,103.34 \end{gathered}[/tex]

Therefore, James needs to invest $3,103.34 as his principal in order to achieve the goal.

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