Final answer:
To calculate the interest rate of an account with continuous compounding, we use the formula A = Pert to solve for r, which represents the interest rate. In Adam's investment scenario, by substituting the given values into the rearranged formula r = (1/t) ln(A/P), we can find the interest rate after calculating the natural logarithm of the growth factor and dividing by the time period.
Step-by-step explanation:
The question asks us to determine the interest rate of an account that compounds continuously. Adam has invested $10,000 and after 9 years, it has grown to $18,000. To find the interest rate, we would use the formula for continuous compounding interest which is A = Pert, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial sum of money), r is the annual interest rate (in decimal), t is the time the money is invested for, and e is the base of the natural logarithm.
In this case, we have A = $18,000, P = $10,000, and t = 9 years. Rewriting the formula to solve for r, we get r = (1/t) ln(A/P). Plugging in the values we get r = (1/9) ln(18,000/10,000) = (1/9) ln(1.8). The result after calculating the natural logarithm of 1.8 and dividing by 9 will give us the annual interest rate in decimal form.