Question

A person places $1150 in an investment account earning an annual rate of 5.3%, compounded continuously. Using the formula V = Pe^{rt}V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 10 years.

Answer 1

The amount of money in the account after 10 years is approximately $1844.86.

Step-by-step explanation:

To find the amount of money in the account after 10 years, we can use the formula V = Pert. In this case, the principal (P) is $1150, the rate (r) is 5.3% (or 0.053 as a decimal), and the time (t) is 10 years. Plugging these values into the formula, we have V = 1150 * e0.053 * 10. Using a calculator, we can evaluate this expression to get V ≈ $1844.86. Therefore, the amount of money in the account after 10 years is approximately $1844.86.