Question 332248: Suppose that $2000 is invested at a rate of 6% per year compounded continuously. What is the balance after 1 yr? After 2 yrs?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Recall that the formula for continuous compounding interest is
where A is the return, P is the principal (amount invested), r is the interest rate (in decimal form) and t is the time in years.
Since "$2000 is invested at a rate of 6% per year compounded continuously", we know that  and  (the decimal equivalent of 6%).
Now let's compute the return when  (ie find the balance after one year)
Start with the continuous compounding formula.
 Plug in , , and .
 Multiply  and  to get .
 Raise 'e' (which is approximately 2.71828) to the power to get  (this value is approximate).
 Multiply  and to get  .
 Round to the nearest hundredth (ie to the nearest penny).
So after 1 year, you'll have about $2,123.67
-----------------------------------------------------------------------------
Now let's compute the return when  (ie find the balance after two years)
Start with the continuous compounding formula.
 Plug in , (the decimal equivalent of 6%), and .
 Multiply and  to get  .
 Raise 'e' (which is approximately 2.71828) to the power to get  (this value is approximate).
 Multiply and to get  .
 Round to the nearest hundredth (ie to the nearest penny).
So after two years, you'll have $2,254.99
|
|
|
