You have decided to purchase your first house with the help of a $$400,000$ mortgage from your bank. The interest rate offered is $3\mathrm{.}2\%$ per year, compounded semi$-$annually. The mortgage is amortized over $25$ years and you have decided to make monthly payments.

i$)$ What is the amount of your monthly payment?

ii$)$ Assume that after $5$ years the bank renews the terms of your mortgage with the same interest rate. What is the outstanding balance on your mortgage after $5$ years of payments?

iii$)$ How much interest has been paid over the first $5$ years of your mortgage?

iv$)$ After the first $5$ years of your mortgage, you decide to increase your monthly payment by $$200$ per month. How many years will it now take you to pay off your mortgage?