Part $2$: Application

$6.$ You decide to borrow $$23000$ to do some renovations on your home. You are comparing two options.

Option A: Monthly payments for three years at $2\mathrm{.}5\%$ financing compounded monthly.

Option B: Monthly payments for five years at $3\mathrm{.}5\%$ financing compounded monthly.

a$)$ What is the monthly payment for Option A$?$

b$)$ What is the monthly payment for Option B$?$

c$)$ Give one logical reason for choosing option A and one logical reason for choosing option