Final answer:
To determine at the end of how many years the buyer will be able to drop the PMI, we need to calculate when the Loan-to-Value (LTV) ratio reaches 75%. The buyer pays off $10,000 per year on the loan. By solving the equation, we can find the value of x, which represents the number of years it will take for the LTV ratio to reach 75%.
Step-by-step explanation:
To determine at the end of how many years the buyer will be able to drop the PMI, we need to calculate when the Loan-to-Value (LTV) ratio reaches 75%. The initial LTV ratio is 100% because the buyer has a 100% financing on a $280,000 house, which means the loan amount is also $280,000.
The buyer pays off $10,000 per year on the loan. So, after x years, the remaining loan amount will be $280,000 - $10,000 * x.
The LTV ratio is calculated by dividing the remaining loan amount by the appraised value of the house. Since the house does not appreciate in value, the appraised value remains the same at $280,000.
The equation to find the LTV ratio is: LTV = (remaining loan amount / appraised value) * 100.
We need to solve the equation: (remaining loan amount / $280,000) * 100 = 75.
Substituting the remaining loan amount, the equation becomes: ($280,000 - $10,000 * x / $280,000) * 100 = 75.
By solving this equation, we can find the value of x, which represents the number of years it will take for the LTV ratio to reach 75% and for the buyer to be able to drop PMI.