Final answer:
To calculate the single payment X needed to settle the loan at the end of 15 years, we would require the annual effective interest rate to perform an amortization calculation over 14 payments and then apply the rate to find the outstanding balance.
Step-by-step explanation:
To find the balance X that the borrower needs to pay at the end of 15 years to settle the loan, we must first find the scheduled periodic payments and the outstanding loan balance after 14 payments. Given that the loan amount is $800,000 and 20 end-of-year payments of $55,000 are made, the question is essentially asking for a loan amortization calculation which would involve the annual effective interest rate (not provided in the question).
Since the interest rate is not specified, we can represent it as i. With the interest rate, we would first calculate the present value of the 14 payments made as scheduled using a present value formula for an annuity. After deducting this amount from the initial loan, we'd obtain the accumulated value of the remaining loan after 14 years. Next, we'd apply the interest rate to this value to find the balance after 15 years, or X.
The exact calculation requires specific details such as the interest rate, which is not provided in the context. Without this critical information, we're unable to calculate the precise payoff balance X.