Final answer:
To find the balance after 8 years for a $400 deposit with a 5.5% interest rate compounded continuously, use the formula A = Pe^rt and insert the given values. After calculation, you can determine the total balance in the account.
Step-by-step explanation:
To calculate the balance of $400 deposited in an account with a 5.5% interest rate, compounded continuously after 8 years, we can use the formula for continuous compounding:
A = Pert
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- t is the time the money is invested for, in years.
- e is the base of the natural logarithm, approximately equal to 2.71828.
First, we convert the interest rate from a percentage to a decimal by dividing by 100:
r = 5.5% / 100 = 0.055
Now we can insert the values into the formula:
A = 400e(0.055*8)
A = 400 * e0.44
A = 400 * 2.718280.44
After calculating the value of e raised to the power of 0.44, we multiply the result by 400 to find the total amount.
Therefore, the balance after 8 years will be the result of the above calculation.