Final answer:
To calculate the interest component of payment 206, use the compound interest formula to determine the remaining balance on the loan, then subtract it from the loan amount. The negative value indicates that the loan will not be completely paid off by that payment.
Step-by-step explanation:
To calculate the interest component of payment 206, we first need to determine the remaining balance on the loan at that time. Since the loan is compounded semiannually, we can use the compound interest formula:
Balance = Principal x (1 + (Rate / n))^(n x t)
Where Principal = $106,000, Rate = 7.9%, n = 2 (semiannual compounding), and t = 206 months / 12 = 17.17 years. Plugging in the values, we get:
Balance = $106,000 x (1 + (0.079 / 2))^(2 x 17.17) = $363,614.04
Next, we can calculate the interest component of payment 206 by subtracting the remaining balance from the loan amount:
Interest Component = $106,000 - $363,614.04 = -$257,614.04
Since the monthly payments are $780, the interest component of payment 206 is negative, indicating that the loan will not be completely paid off by that payment.