You deposit $800 in an account that pays 5.5% annual interest compunded continuously. Find the balance at the end of 5 years.
Am i correct in using this formula?
A=pe^(rt)
The formula is correct.
Post your answer for check if you wish.
Yes, you are correct in using the formula A = P * e^(rt) to find the balance at the end of 5 years for an account with continuous compounding interest.
Here's how you can apply the formula to solve the problem:
A = P * e^(rt)
Where:
A = the balance at the end of the time period
P = the initial principal (initial deposit)
e = Euler's number, approximately 2.71828
r = the annual interest rate (in decimal form)
t = the time period in years
In this case, P = $800, r = 5.5% which is equivalent to 0.055 in decimal form, and t = 5 years.
So, substituting these values into the formula, we have:
A = 800 * e^(0.055 * 5)
Now, calculate the value of e^(0.055 * 5) using a calculator:
e^(0.055 * 5) ≈ 1.30514
Finally, substitute this value back into the formula:
A = 800 * 1.30514
Calculating this, we get:
A ≈ $1,044.12
Therefore, the balance at the end of 5 years would be approximately $1,044.12.