Final answer:
After selling the home for $510,000 and incurring an 8% cost for commissions, taxes, and fees, you would be left with $69,200, which is less than the initial downpayment of $100,000.
Step-by-step explanation:
Let's calculate the amount that will be returned from the original downpayment after selling the home. If you originally bought the home for $500,000 and made a $100,000 downpayment, borrowing the remaining amount with a mortgage, and then one year later, the value of your home appreciated by 2%, the selling price would be: $500,000 × 1.02 = $510,000.
However, selling a home typically incurs additional costs such as real estate commissions, taxes, and fees, which in this scenario amount to 8% of the selling price. Therefore, the total cost of these expenses would be: $510,000 × 0.08 = $40,800.
The net amount received from the sale, after subtracting these costs, would be: $510,000 - $40,800 = $469,200. Since we've ignored the small amount of the principal paid on the mortgage during the first year, we still assume an outstanding loan amount of $400,000. This means that upon selling the house, you would need to repay this amount to the bank.
After repaying the mortgage, the remaining amount from the sale proceeds would be: $469,200 - $400,000 = $69,200. This amount represents how much of your original downpayment you would get back, which, in this case, is less than the $100,000 initially put down.