$2.$ You obtain a loan of $$500,000$ from a bank to buy a house. The mortgage has a $5-$

year term with a fixed rate of $5\%/$year $($using Canadian mortgage convention$).$ The

amortization period of the mortgage is $20$ years.

$($a$)$ What is the monthly mortgage payment?

$($b$)$ How much do you owe the bank after the $60$th monthly payment?

$($c$)$ For the $26$th monthly payment, how much of it is for interest, and how much of

it is for principal repayment?

$($d$)$ Find the expression for the present value of the principal repayment for the month

t mortgage payment $($i$.$e$.,$ a general expression for any given month t$).$ Is this

present value constant over different months? What is the total present value of

the interest portion of the $60$ mortgage payments?