Take home quiz?

So, I’ve been PMing sir hoping that he’d be able to answer my inquiries. 😔 I sound like a nerd… 

Sir, I know how to get the APR already (I input some random number in the interest rate, calculated the monthly payment based on the rate, did the loan schedule, and then decided to use trial and error to input a number which will generate a monthly payment relatively equal to the given amount in the loan matrix. I suppose there’s no shortcut to calculate APR?).

But I’m confused with the Ave. use of money.
Do we use 1st month BEGINNING balance + Last month BEGINNING balance all divided by 2 or 1st month ENDING balance + Last month ENDING balance all divided by 2?
In this case,  (100,000 + 9070.06)/2 = 54,535.03 or (92,365.90+0.022)/2 = 46,182.96 po? Just getting confused po.
Pls see attached file po. I tried solving number 2 already po eh.
Thanks, sir!

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