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Jennifer invested $5,000 in her savings account for 7 years. When she withdrew it, she had $7,825 89 Interest was compoundedcontinuously. What was the interest rate on the account? Round to the nearest tenth of a percent

Respuesta :

We are told that the interest is compounded continuously, therefore, we use the following formula:

[tex]A=Pe^{rt}[/tex]

Where "A" is the present value, "P" the initial value, "r" the interest rate, and "t" the time:

Now we solve for "r", first by dividing both sides by "P":

[tex]\frac{A}{P}=e^{rt}[/tex]

Now we take natural logarithm to both sides:

[tex]\ln \frac{A}{P}=rt[/tex]

Now we divide both sides by "t":

[tex]\frac{1}{t}\ln \frac{A}{P}=r[/tex]

Now we replace the given values:

[tex]\frac{1}{7}\ln \frac{7825.89}{5000}=r[/tex]

Solving the operations we get:

[tex]0.063=r[/tex]

Therefore, the interest rate is 6.3%.

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