Question

An initial amount of $3600 is invested in an account at an interest rate of 8% per year, compounded continuously. Assuming that no withdrawals are made, find the amount in the account after three years.

Answer 1

The formula for calculating the balance of an account with continuous compounding is given by A = Pe^(rt), where A is the final amount, P is the initial principal balance, r is the annual interest rate (expressed as a decimal), t is the time in years, and e is the mathematical constant approximately equal to 2.71828.

In this case, the initial principal balance P is $3600, the annual interest rate r is 8% or 0.08 as a decimal, and the time t is 3 years. Plugging these values into the formula gives us:

A = 3600 * e^(0.08 * 3)

Evaluating this expression gives us a final amount of approximately $4293.25 in the account after three years.