Question $7(6$points$)$

A construction company decided to purchase excavation equipment. The company paid $$10,000$

of the equipment price as a down payment and took the remaining as a loan from a local bank over

fifteen years contract period. The bank approved the loan, that the company must pay it back in

equal monthly payments beginning one month after the third $"3"$t years of the contract period,

with an effective interest rate of $4\mathrm{.}0604\%$ compounded quarterly. If the value of the equipment at

the end of the fifteen$-$years period is $$158,052\mathrm{.}6$

Calculate the following:

i$)$ The nominal interest rate.

$[2$marks$]$

ii$)$ The monthly payment.