Answer :
In the context of home purchase, the factor that provides instant equity in a home after purchase is the down payment.
1. **Down Payment:**
- When you make a down payment on a home, you are paying a portion of the purchase price upfront, reducing the amount you need to borrow from a lender.
- This upfront payment immediately increases your ownership stake in the property, creating instant equity in the home.
- For example, if you buy a $200,000 home and make a $40,000 (20%) down payment, you instantly have $40,000 in equity in the home ($40,000 down payment + $0 borrowed = $40,000 equity).
The other options listed do not provide instant equity in a home after purchase:
- **Depreciation:** Depreciation refers to a decrease in the value of an asset over time, which is not relevant to gaining instant equity in a home.
- **Mortgage Insurance:** Mortgage insurance is a policy that protects the lender in case the borrower defaults on the loan; it does not contribute to instant equity for the homeowner.
- **Interest:** Interest is the cost of borrowing money and is paid to the lender over time; it does not directly impact the equity in the home.
Therefore, the down payment is the key element that immediately increases your ownership stake and provides instant equity in a home after purchase.