Find the time required for an investment of 5000 dollars to grow to 6800 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.

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03-11-2022
Mathematics

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Find the time required for an investment of 5000 dollars to grow to 6800 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.

Sagot :

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ElimelechW638935 ElimelechW638935 · Answer 1 · 2022-11-03T02:56:01-04:00

Given

The initial investment is given 5000 dollar , interest rate is 7.5 percent per year compounded quarterly.

Required

To determine the time required to grow the initial investment of 5000 dollar to 6800 dollar.

Explanation

The formula for the amount ,

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

For compounded quarterly , n=4.

Substitute the values.

[tex]\begin{gathered} 6800=5000(1+\frac{7.5}{100\times4})^{4\times t} \\ \frac{68}{50}=(1+0.01875)^{4t} \\ 1.36=1.01875^{4t} \end{gathered}[/tex]

Take ln both sides.

[tex]\begin{gathered} ln1.36=4tln1.01875 \\ 4t=\frac{0.3074}{0.018576} \\ 4t=16.54 \\ t=4.137 \end{gathered}[/tex]Answer

Hence the time required for an investment of 5000 dollars to grow to 6800 dollars at an interest rate of 7.5 percent per year, compounded quarterly is 4.14 years.

Sagot :

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