Question

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

Answer 1

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

`A=Pe^(rt)`

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":

`(A)/(P)=e^(rt)`

Now we take natural logarithm to both sides:

`\ln (A)/(P)=rt`

Now we divide both sides by "t":

`(1)/(t)\ln (A)/(P)=r`

Now we replace the given values:

`(1)/(7)\ln (7825.89)/(5000)=r`

Solving the operations we get:

`0.063=r`

Therefore, the interest rate is 6.3%.