You are planning to invest $500 in a savings account and are deciding between two options. Account #1 earns 2.9% annual interest and is compounded continuously. Account #2 earns 3.1% annual interest and compounded monthly. Which savings account will yield the greater amount after 5 years?

Option 1 has a return of about $899.13

Option 2 has a return of $582.46

Option 1 is better

Step-by-step explanation:

This is the work =  $899.13 shown which plugged into desmos gets that result. For the second equation i just did it like 500*1.031= until i got the answer of 582.456278117 or rounded to $582.46

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584