You deposit $800 in an account that pays % annual interest compounded
continuously. Find the balance at the end of 5 years.
if you meant r%, then
800e^(5r/100)
To find the balance at the end of 5 years, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the final amount/ balance
P = the principal amount (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, the principal amount (P) is $800, the annual interest rate (r) is given as a percentage, and the time period (t) is 5 years.
First, we need to convert the annual interest rate from a percentage to a decimal. Since the interest rate is given as a percentage, we divide it by 100:
r = 5% / 100 = 0.05
Next, we can substitute the given values into the formula:
A = 800 * e^(0.05 * 5)
To calculate this value, we need the value of Euler's number (e) raised to the power of (0.05 * 5).
Using a calculator, we get e^(0.05 * 5) ≈ 1.28347.
Now, we can substitute this value back into the formula:
A = 800 * 1.28347
Calculating this, we get:
A ≈ 1026.78
Therefore, the balance at the end of 5 years would be approximately $1026.78.