You deposit $800 in an account that pays 5.5% annual interest compounded
continuously. Find the balance at the end of 5 years.
a whole new post, why not just add the correction to the original post?
800e^(0.055*5) = ____
To find the balance at the end of 5 years with continuous compounding, we can use the formula:
A = P * e^(rt)
Where:
A = the balance at the end of the time period
P = the initial principal (the amount you deposited)
e = Euler's number, approximately 2.71828
r = the annual interest rate (as a decimal)
t = the time in years
In this case, the initial principal (P) is $800, the annual interest rate (r) is 5.5% or 0.055 as a decimal, and the time period (t) is 5 years.
Substituting these values into the formula, we have:
A = 800 * e^(0.055 * 5)
Calculating this using a calculator or a math software, we find:
A ≈ 800 * 2.71828^(0.275)
A ≈ 800 * 1.31773
A ≈ $1,054.18
Therefore, the balance at the end of 5 years with continuous compounding will be approximately $1,054.18.
To find the balance at the end of 5 years with continuous compounding, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the balance after time t
P = the principal amount (initial deposit)
e = the mathematical constant approximately equal to 2.71828
r = the annual interest rate (in decimal form)
t = the time in years
In this case, P = $800, r = 5.5% = 0.055, and t = 5 years. We can substitute these values into the formula and solve for A.
A = $800 * e^(0.055 * 5)
First, calculate the value of the exponent:
0.055 * 5 = 0.275
Next, calculate e^(0.275):
e^(0.275) ≈ 1.316151
Finally, multiply the principal amount by the result to get the balance at the end of 5 years:
A ≈ $800 * 1.316151 ≈ $1,052.92
Therefore, the balance at the end of 5 years with continuous compounding is approximately $1,052.92.