Final answer:
To find the balance remaining after 3 years on a fixed-rate mortgage of an initial $300,000 (after a $100,000 downpayment on a $400,000 house), you would typically use the amortization formula, requiring knowledge of the interest rate and payment frequency, none of which are provided in the question.
Step-by-step explanation:
Finding the Balance After 3 Years
When you bought a house for $400,000 and made a downpayment of $100,000, the remaining balance of $300,000 is what you need to pay back through annual payments. If we assume a fixed annual payment and interest rate, after 3 years you will have made a certain amount in payments, and the balance would be the initial loan minus the principal part of these payments. Without the interest rate provided, we cannot calculate the exact remaining balance. In general, for a fixed-rate mortgage, you would use the amortization formula to determine the remaining balance:
PV = R × {(1 - (1 + i)^-n) / i}
Where:
PV = Present Value or the loan amount remaining
R = Annual Payment
i = interest rate per period
n = number of periods remaining
The formula combines the initial loan amount, the payments you make, and the interest that accumulates over the time to find the balance. Since the interest rate and the payment frequency are not mentioned, we cannot provide the balance after 3 years.