you invest $2800 in an account that pays an interest of 5.5%, compounded continuously. calculate the balance of your account after 12 years.
FV = 2800e^(.055*12)
FV = 2800e^(.66) = 5417.42
To calculate the balance of an investment with continuous compounding, you can use the formula:
A = P * e^(rt)
Where:
A = the ending balance of the investment
P = the principal amount (initial investment)
e = Euler's number (approximately 2.71828)
r = the interest rate per period (expressed as a decimal)
t = the number of periods (in this case, years)
In your case, the principal amount (P) is $2800, the interest rate (r) is 5.5% or 0.055 (expressed as a decimal), and the number of years (t) is 12.
Substituting these values into the formula:
A = 2800 * e^(0.055 * 12)
To calculate this using a calculator, you need to use the exponent button or the "^" symbol. Raise Euler's number (e) to the power of (0.055 * 12):
A ≈ 2800 * e^(0.66)
Calculating the exponent first:
A ≈ 2800 * 1.9367736
And finally, multiply this by the principal amount:
A ≈ $5,412.68
So, the balance of your account after 12 years would be approximately $5,412.68.
To calculate the balance of your account after 12 years with continuous compounding, we can use the formula:
A = P * e^(rt)
Where:
A = the final account balance
P = the initial investment amount
r = the interest rate (expressed as a decimal)
t = the time period in years
e = Euler's number (approximately 2.71828)
Given that:
P = $2800
r = 5.5% = 0.055 (as a decimal)
t = 12 years
Now we can substitute the values into the formula:
A = 2800 * e^(0.055 * 12)
Using a calculator, we can evaluate the exponential part of the formula:
A ≈ 2800 * e^(0.66)
A ≈ 2800 * 1.93261622
A ≈ $5,408.97
Therefore, the balance of your account after 12 years would be approximately $5,408.97.