you deposit $2200 in an account that pays 3% interest, after 15 years you withdraw, what is the balance if the interest is compounded continuously

3500

To find the balance of an account with continuously compounded interest, you can use the formula:

A = P * e^(rt)

Where:
A is the final balance,
P is the initial principal (amount deposited),
e is the mathematical constant approximately equal to 2.71828,
r is the interest rate (in decimal form),
and t is the time in years.

In this case, P = $2200, r = 3% = 0.03, and t = 15 years.

First, let's plug in the values and calculate the result step by step:

A = $2200 * e^(0.03 * 15)

To calculate e^(0.03 * 15), you can use a scientific calculator or spreadsheet software.

e^(0.03 * 15) ≈ 2.85677399903

Now, substitute the value into the formula:

A = $2200 * 2.85677399903

Calculating the final balance:

A ≈ $6288.90

So, if the interest is continuously compounded, the balance after 15 years with an initial deposit of $2200 and a 3% interest rate would be approximately $6288.90.