Question

A woman invests $6300 in an account that pays 6% interest per year, compounded continuously.(a) What is the amount after 2 years? (Round your answer to the nearest cent.)$ (b) How long will it take for the amount to be $8000? (Round your answer to two decimal places.) yr

Answer 1

Given: A woman invests $6300 in an account that pays 6% interest per year, compounded continuously.

Required: a) To determine the amount after 2 years.

b) To determine how long it will take for the amount to be $8000.

Step-by-step explanation: The amount, A after t years with an interest rate of r is given by-

`A=Pe^(rt)`

Here,

`\begin{gathered} P=6300 \\ r=(6)/(100) \\ =0.06 \\ t=2 \end{gathered}`

Substituting the values, we get-

`\begin{gathered} A=6300e^(0.06*2) \\ =7103.23 \end{gathered}`

Hence the amount after 2 years is $7103.23

Next, let t be the time it takes for the amount to be $8000-

`\begin{gathered} 8000=6300e^(0.06t) \\ (8000)/(6300)=e^(0.06t) \\ \ln(1.2698)=0.06t \end{gathered}`

Further solving for t as-

`t=3.98\text{ years}`

Hence, it takes 3.98 years for the amount to be $8000.

Final Answer: a) $7103.23

b) 3.98 years