Question

Formula is A= Pe^rt round on the seventh number each time if needed

Answer 1

The person deposited $800 in a continuously compounded accont for 5 years, at the end of which she had accumulated $1162.00.

We are asked to find the iterest rate.

We use the formula for accumulated amount in a continuously compounded interest rate account:

`A=P\cdot e^(r\cdot t)`

where r is the unknown interest rate,

P is the principal (in our case 800)

A is the total amount accumulated (in our case 1162)

and t is 5 (for the 5 years)

So in order to solve for the rate "r" which is in the exponent, weproceed by first dividing both sides by 800, and then using the natural log function (ln) to bring the exponent down, as shown below:

`\begin{gathered} 1162=800\cdot e^(r\cdot5) \\ (1162)/(800)=e^(r\cdot5) \\ \ln ((1162)/(800))=r\cdot5 \\ r\text{ = }\ln ((1162)/(800))(1)/(5) \\ r\approx0.074657 \\ \end{gathered}`

this decimal corresponds to a 7.4657% and since we are asked to round the percent to the tenth, we answer: 7.5%.