Entity A issued $$5,000,000$ of $6\%,10-$year bonds on January $1,2024,$ for $$4,328,974$ to yield an effective annual rate of $8\%.$ Interest is payable annually on January $1.$ The effective$-$interest method of amortization is to be used. You can round to the nearest dollar.

A$.$ Prove that the amount received for the bonds is correct

I am attaching the next example:

Bond Interest Expense$-$Amortize

Discount

$$ Suppose we have a $$10,0005-$year bond paying $8\%$ annual interest

issued $1/1/2022$ when the market rate was $9\%.$ The bond sold for

$96\mathrm{.}11$

$$ Proof:

Prin. $10,000*$PVIF$,9\%,5$ per. $(\mathrm{.}64993)=6,499$

Pymts $800*$PVAN$,9\%,5$ per. $(3\mathrm{.}88965)=3,112$

$9,611$

I can't figure out the formula used at the example to reach that conclusion, could yo develop the result using the first information?