Final answer:
Using the continuous compounding interest formula, with a principal of $85,800 at an annual rate of 8.5% over 9 years, the future value of the investment will be approximately $158,336.11.
Step-by-step explanation:
The question involves calculating the future value of an investment using the continuous compounding interest formula: V = Pert, where V is the future value of the investment, P is the principal amount, e is the base of the natural logarithm (approximately 2.71828), r is the annual interest rate (expressed as a decimal), and t is the number of years the money is invested. To calculate the amount of money in the account after 9 years with a principal of $85,800 and an annual interest rate of 8.5%, we can plug the values into the formula:
V = $85,800 × e(0.085×9)
Using a calculator with an exponent function for e, you would compute the exponent first, then multiply by the principal:
V = $85,800 × e0.765
After calculating the exponent and rounding to the nearest cent:
V ≈ $158,336.11
Thus, the account will have approximately $158,336.11 after 9 years.