Sam is considering investing in a bond with a face value of $$10,000.$ The bond pays a coupon

interest of $4\%$ payable quarterly. If he expects to make a return equal to market interest rate of $1$

$\%$ per quarter on this investment with a maturity of $15$ years, determine the most he can pay for

the bond. Find

i$)$ quarterly coupon interest payment amount.

ii$)$ i per quarter and n$.$

iii$)$ price he can offer for the bond.