Grant Co$.$ issued $$500,000$ face$-$value, five$-$year, $8$ percent bonds on December $31,$ Year $1.$

The bonds pay interest annually, and were sold to yield $7$ percent. Present value factors are as follows:

$7\%8\%$

Present value of $$1,$ five periods $0\mathrm{.}7129860\mathrm{.}680583$

Present value of ordinary annuity of $$1,$ five periods $4\mathrm{.}1001973\mathrm{.}992710$

Present value of annuity due of $$1,$ five periods $4\mathrm{.}3872114\mathrm{.}312127$

What amount of long$-$term liability should Grant report on December $31,$ Year $1,$ for this sale?

A$.$ $$500,000$ B$.$ $$512,777$ C$.$ $$520,501$ D$.$ $$531,981$

Note:

Please provide DETAIL Explanation

$1.$ On why the $7\%$ Present values were considered for calculation against the $8\%.$

$2.$ Let me know the situation when the PV of Ordinary Annuity and PV of Annuity due should be used.