Answered

Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Experience the convenience of getting accurate answers to your questions from a dedicated community of professionals. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

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.

Find The Time Required For An Investment Of 5000 Dollars To Grow To 6800 Dollars At An Interest Rate Of 75 Percent Per Year Compounded QuarterlyYour Answer Is T class=

Sagot :

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.

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.