Final answer:
Hilary's rate of return on her investment for the year is -4%.
Step-by-step explanation:
To calculate the rate of return on Hilary's investment, we need to consider the initial cost of the house, the down payment, the mortgage amount, and the selling price after the decline in value.
Hilary bought the house for $100,000 and put down 20% of the price, which is $20,000. So, she took a mortgage loan of $80,000. Her mortgage interest rate is 8% per year.
After 1 year, the house has declined in value by 4%. This means the selling price is 4% less than the original price. So, the selling price is $100,000 - (0.04 * $100,000) = $96,000.
Now, let's calculate the rate of return based on the initial investment and the selling price. The initial investment is the down payment plus the mortgage amount: $20,000 + $80,000 = $100,000. The return on investment is the difference between the selling price and the initial investment: $96,000 - $100,000 = -$4,000.
Since the return is negative, Hilary has incurred a loss on her investment. We can calculate the rate of return by dividing the loss by the initial investment and multiplying by 100 to get a percentage: (-$4,000 / $100,000) * 100 = -4%.
Therefore, the rate of return on Hilary's investment for the year is -4%.