Question

Robert invested $800 in a bank account. the account has an annual interest of 5.5% that is compounded continuously. how much money will be in the account after 12 years?

Answer 1

Using the formula for continuous compounding, A = Pert, the calculation shows that after 12 years, Robert's initial $800 investment at a 5.5% annual interest rate will grow to approximately $1548.40.

Step-by-step explanation:

To calculate the future value of an investment with continuous compounding, we use the formula A = Pert, where P is the principal amount, r is the annual interest rate, t is the time in years, and e is the base of the natural logarithm, approximately equal to 2.71828.

For Robert's investment of $800 at an annual interest rate of 5.5% (or 0.055 when expressed as a decimal) compounded continuously for 12 years, the formula becomes:

A = 800e0.055*12

Next, we calculate the value inside the exponent:

0.055*12 = 0.66

Now we raise e to the power of 0.66:

e0.66 ≈ 1.93550

And finally we multiply by the principal:

A = 800 * 1.93550 ≈ $1548.40

After 12 years, Robert will have approximately $1548.40 in his account.