Final answer:
The smallest negative effect on a credit score when looking to finance a home at the best rate comes from paying off a car loan. The other options can have varying degrees of negative impact, with missing a mortgage payment being the most detrimental to a credit score.
Step-by-step explanation:
When looking to finance a home with the best possible rate, the option with the smallest negative effect on your credit score is paying off a car loan (C). Paying off a car loan can exhibit financial responsibility and the ability to manage and repay debt, which could have a positive, or at worst, neutral effect on your credit score. In contrast, missing a mortgage payment (D) would have a severe negative impact, potentially leading to a significant drop in your credit score. Opening a new credit card (B) can lead to a hard inquiry on your credit report, which might lower your score slightly in the short term. Closing a credit card account (A) can affect your credit utilization ratio and the length of your credit history, both of which are important factors in calculating your credit score, potentially reducing it depending on your overall credit profile.