Series Question (1 Viewer)

[Green Yoda]

https://cdn.discordapp.com/attachments/196506248953200640/254497553943363584/IMG_4183.JPG

Can someone help me with b (i)?

 

[android0]

At the start of the first month, she already has $55 772, but instead of adding her usual amount, she adds $M.
Beginning of month 1: $55 772 + $M

So A1 = ($55 772 + $M) x 1.005

A2 = (A1 + $M) x 1.005

A2 = [[($55 772 + $M) x 1.005] + $M] x 1.005

A2 = [($55 772 + $M) x 1.005^2 + $1.005M

A2 = (1.005^2)($55 772) + $(1.005^2)M + $1.005M

A2 = ($55 772)(1.005^2) + $M(1.005 + 1.005^2)