Final answer:
Calculating the number of months it will take to pay off a bill with monthly installments and interest involves an amortization calculation, which can be complex due to the monthly compounding interest on the reducing balance. It necessitates the use of a financial calculator or spreadsheet software.
Step-by-step explanation:
To determine the number of months it will take to pay off the account balance on a bill of $14,598.58 with monthly installments of $320 and a monthly interest rate of 0.9%, we need to set up an amortization calculation. This calculation involves both the reduction of the balance with each payment and the addition of interest to the remaining balance. Because the interest rate can cause the balance to decrease at a slower rate, calculating the exact number of months requires either a complex formula or the use of financial calculator software.
Given that each month's interest adds to the balance and the constant payment reduces it, the payment might not be sufficient to cover the interest in early stages if it's too low, prolonging the time to pay off the debt. This is similar to why a $20,000 loan with monthly payments less than the monthly interest never reduces the principal.
Due to the complexity of such calculations which take into account variable interest compounding monthly on the reducing balance, the exact duration would typically be determined using a financial calculator or spreadsheet software designed to perform amortization of loans with interest, which provides a schedule of payments until the loan is paid off. Without such tools, we cannot provide an exact number of months it will take to pay off the balance in this situation.