Retirement Plan: Eric needs to deposit an amount $($let$$s call it $R$)$ into a savings account with a

$4\%$ monthly compound interest rate until he turns $55.$ After $10$ years, the account will continue to

accrue interest at an annual rate of $4\mathrm{.}5\%.$ When he reaches $65,$ the interest rate remains constant at

$5\%.$ At that point, he wants to receive $$5,000$ per month for $20$ years.

You are tasked with explaining the monthly deposit amounts for two refinance products to Eric,

who is currently $35$ years old. Additionally, you need to provide information about the monthly

deposit amount $($$R$)$ for a retirement plan over the next $20$ years. To determine the required

amounts, you must address the following questions in your letter:

a$.$ Calculate the monthly payment and the total amount saved if Eric switches to Product A$.$

b$.$ Calculate the monthly payment and the total amount saved if Eric switches to Product B$.$

c$.$ Determine the amount needed for Eric, who turns $65,$ to receive $$5,000$ monthly over the

next $20$ years.

d$.$ Calculate the amount Eric, at $55$ years old, needs to prepare.

e$.$ Decide the monthly deposit amount Eric needs to make from now until the age of $55$ for

the next $20$ years.

f$.$ Calculate the minimum profit Eric needs to earn monthly to pay the bank's loan and save

for the retirement plan.

g$.$ If you have any suggestions on how to make Eric perceive your product more attractively,

please propose your ideas. For example, considering a $50\%$ discount on refinance fees if

both refinance and pension plans are chosen.