Wendy wins $5000. She wishes to invest her winnings. Which one gives her the greater total at the end of time? Choice 1: 8.5% p.a. simple interest for 4 years

Nice try, GoldenLeaf, but I believe you gave compound interest.

The formula for simple interest is:

I = Prt   where P is what we invest, r is the rate, and t is the time in years.

So in the first case. we have

I = 5000(.085)(4) = $1700

In the second case, we have

I = 5000(.08)(4.5) = $1800 ......(54 months  = 4.5 years)

Choice 2 is better. Note that the amount we start with doesn't matter. (.085)(4) = .34,  but (.08)(4.5) = .36. So, as long as we start with the same amount, Choice 2 is always better!!

This is a compare and contrast problem.

$${\mathtt{5\,000}}{\mathtt{\,\times\,}}{\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{0.085}}}{{\mathtt{12}}}}\right)}^{{\mathtt{48}}} = {\mathtt{7\,016.323\: \!774\: \!833\: \!980\: \!751\: \!8}}$$

$${\mathtt{5\,000}}{\mathtt{\,\times\,}}{\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{0.08}}}{{\mathtt{12}}}}\right)}^{{\mathtt{54}}} = {\mathtt{7\,158.090\: \!240\: \!747\: \!356\: \!130\: \!5}}$$

Thus, Choice 2 is the correct answer.

Okay, I just remembered that I needed to add the '/12' there since we are going my monthly interest I presume?