Question

suppose that $2500 is deposited in a savings account paying 5% interest, compounded continuously. What will be the average value of the count during the next 10 years

Answer 1

E none of these

Step-by-step explanation

The continuous compounding formula says

`\begin{gathered} A=P*e^(rt) \\ where \\ A\text{ is the final amount} \\ Pis\text{ the initial amount} \\ r\text{ is the rate of interest} \\ t\text{ is the time} \end{gathered}`

so

Step 1

find the final amount:

a)Let

`\begin{gathered} P=2500 \\ r=5\text{ \% = }(5)/(100)=0.05 \\ time=\text{ 10 years} \end{gathered}`

b) now, replace

`\begin{gathered} A=Pe^(rt) \\ A=2500(e^(0.05*10)) \\ A=2,500(e^(0.5)) \end{gathered}`

so, the final amout would be:

`A=2,500(e^(0.5))`

Step 2

know to know the average, divide by the numbers of years

so

`\begin{gathered} average=(P)/(time) \\ Average=(2500(e^(0.5)))/(10) \\ Average=250(e^(0.5)) \end{gathered}`

so, the answer is

E none of these

I hope this helps you