Using continuous compounding. A 13,000 deposit in an account with APR of 4.5 percent is. The balance in the account after 1 year is what.
P=ert
13000=e.045(1)
To find the balance in the account after 1 year with continuous compounding, we can use the formula:
A = P * e^(rt)
Where:
A = the final balance in the account
P = the initial deposit
r = the annual interest rate (expressed as a decimal)
t = the time period in years
e = Euler's number (approximately 2.71828)
Given:
P = $13,000
r = 4.5% = 0.045 (after converting to a decimal)
t = 1 year
Now, let's substitute these values into the formula to find the balance in the account after 1 year:
A = 13,000 * e^(0.045 * 1)
To calculate the value of e^(0.045), you can use a scientific calculator or an online calculator. The result is approximately 1.046646.
A ≈ 13,000 * 1.046646
A ≈ $13,595.49
Therefore, the balance in the account after 1 year, with continuous compounding, is approximately $13,595.49.