you deposit $2200 in an account that pays 3% annual interest. after 15 years, you withdraw the money.
what is the balance if the interest is compounded continuously?
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To calculate the balance of an account with continuous compounding, you can use the formula:
A = P * e^(rt),
where:
A = the final amount or balance
P = the initial principal amount ($2200 in this case)
e = the base of the natural logarithm (approximately equal to 2.71828)
r = the annual interest rate (3% or 0.03 as a decimal)
t = the time in years (15 years in this case)
Now, let's substitute the values into the formula and calculate the balance:
A = 2200 * e^(0.03*15).
Using a calculator, you can do the following steps:
1. Calculate 0.03 * 15, which equals 0.45.
2. Use the exponential function of your calculator (often denoted as "e^x" or "exp(x)") to find e^(0.45).
3. Multiply the result from step 2 by 2200 to get the final balance.
By following these steps, you should be able to find the balance after 15 years with continuous compounding.