SOLUTION: Suppose that $2000 is invested at a rate of 6% per year compounded continuously. What is the balance after 1 yr? After 2 yrs?

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

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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

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