Please explain, and show me how to get this answer.

Concept Check: Held$-$to$-$Maturity Securities

On July $1,2024,$ Williams issued $$600,000$ of $10\%$ bonds, dated July $1.$ Interest is payable semiannually on June $30$ and December $31.$ The bonds mature in ten years. The market interest rate for bonds of similar risk and maturity is $12\%.$ The entire bond issue was purchased by Joe, Inc. Due to unforeseen circumstances the company decided to sell its debt investment for $$550,000$ on January $1,2026,$ at which time the bonds have an amortized cost of $$580,000.$ Joe's journal entry to record the sale would include a:

a$.$ Credit to cash for $$550,000$

b$.$ Credit to discount on bond investment for $$20,000$

Credit to investment in bonds for $$600,000$

d$.$ Debit to gain on sale of investment for $$30,000$

The correct answer is $c.$

Joe will record the following entry:

Investment in bonds $600,000$