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8. Find the time required for an investment of 5000 dollars to grow to 7900 dollars at an interest rate of 7.5 percent per year, compounded quarterly.Your answer is t=years.You may enter the exact value or round to 2 decimal places.

8 Find the time required for an investment of 5000 dollars to grow to 7900 dollars at an interest rate of 75 percent per year compounded quarterlyYour answer is class=

Respuesta :

Given

Principal = 5000

Amount = 7900

Rate = 7.5%

Find

Time

Explanation

we know the formula of comounded quarterly, is given by

[tex]A=P(1+\frac{r}{400})^{4t}[/tex]

now substitute the values,

[tex]\begin{gathered} 7900=5000(1+\frac{7.5}{400})^{4t} \\ 1.58=(1+0.01875)^{4t} \\ \end{gathered}[/tex]

taking ln both sides,

[tex]\begin{gathered} \ln(1.58)=4t\ln(1.01875) \\ 0.457=4t(0.017) \\ t=\frac{0.457}{4\times0.017} \\ \\ t=\frac{0.457}{0.068} \\ t=6.72 \end{gathered}[/tex]

Final Answer

Therefore , t = 6.72 years

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