Suppose that a vegetable vendor pays 7% interest daily on a $10 loan. Then, suppose that this individual was able to save $0.50 per day by drinking less tea. Calculate the number of days it would take for the vendor to no longer need to borrow money in order to purchase $10 of vegetables (i.e. the day number on which no loan is needed).

To solve this problem, we need to find the number of days it would take for the savings from drinking less tea to accumulate to $10.

Let's break it down step by step:

Step 1: Determine the savings per day:
The vendor saves $0.50 per day by drinking less tea.

Step 2: Calculate the interest earned per day:
The vendor pays 7% interest daily on the loan. This means the vendor earns 7% of the loan amount as interest every day.

Interest earned per day = 7% of $10
= $0.07

Step 3: Calculate the net savings per day after deducting the interest:
Net savings per day = Savings per day - Interest earned per day
= $0.50 - $0.07
= $0.43

Step 4: Calculate the total number of days needed to accumulate $10:
Total number of days = $10 / Net savings per day
= $10 / $0.43

Using a calculator, we find that $10 divided by $0.43 is approximately 23.26.

Hence, it will take approximately 23.26 days for the vendor to accumulate enough savings to no longer need to borrow money and purchase $10 of vegetables.

Since we cannot have a fraction of a day, we can round up the number to the nearest whole number of days.

Therefore, it will take approximately 24 days for the vendor to no longer need to borrow money to purchase $10 worth of vegetables.