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If you put $2,000 into an interest
bearing account, where interest is
compounded quarterly (4 times a year) at
6%, how long will it take for your money
to triple?
Use A = P(1+5)
Solve for t.
t = [?] years
Round your answer to the nearest tenth.

Respuesta :

Answer:

18.4 years

Step-by-step explanation:

The compound interest formula:

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

For this problem we have

[tex]P= 2000\\r= 0.06\\n= 4\\A= 2000(3)= 6000[/tex]

We plug our numbers...

[tex]6,000= 2,000(1+\frac{0.06}{4} )^{4t} \\[/tex]

Then divide

[tex]6,000/2,000=3[/tex]

[tex]3= (1.015)^{4t}[/tex]

Apply log both sides

[tex]3log=(1.015) 4tlog[/tex]

Solve for t

[tex]t= \frac{3log}{(4log(1.015))} =18.4 years[/tex]

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