John borrowed $$400,000$ from a bank to buy an apartment three years ago. He has been paying the monthly

mortgage repayments $($at month end$)$ with an annual fixed interest rate of $5\%$ for three years, and the

mortgage has seven years remaining term. Since the inflation has reverted to the long$-$term target, the Reserve

Bank contemplated cutting the benchmark cash rate. As such, major commercial banks started to offer

special deals to attract new customers. John is considering two deals listed below.

$$ Bank BNZ: a $10-$year mortgage with a fixed interest rate of $4\mathrm{.}8\%$ p$.$a$.$ The monthly mortgage

repayments need to be made at the end of the month. A bonus of $$5,000$ is offered to customers for

transferring an existing mortgage from another bank. $($Hint: the bonus can be used to reduce the

mortgage balance$)$

$$ Bank DBA: an $8-$year mortgage with a fixed interest rate of $4\mathrm{.}8\%$ p$.$a$.$ The quarterly mortgage

repayments need to be made at the beginning of the quarter $($the first repayment is due now$).$ A bonus

of $$4,000$ is offered to customers for transferring an existing mortgage from another bank.

Working as an independent financial planner, you are invited to provide advice about the mortgage decision. In

particular, please advise the following

a$)$ For the existing mortgage, what is the monthly mortgage payment? What$$s the remaining balance?

b$)$ What will be the monthly mortgage repayment if John switches to Bank BNZ$?$ Please construct a loan

repayment table to demonstrate the mortgage account balance over the term of the mortgage.

c$)$ What will be the quarterly mortgage repayment if John switches to Bank DBA? Please construct a loan

repayment table to demonstrate the mortgage account balance over the term of the mortgage.

d$)$ Please advise if should John stay with the current mortgage or switch to a new bank. If switching, which

bank should John move to$?$ Please justify the reasons. $($Hint: considerations should include: total

interest payments and impacts of mortgage repayment on living standard$)$