A manufacturing company is planning to buy a packagin equipment fo $$500,000.$ and make a $$100,000$ own payment $($initial payment at time of purchase$).$ The company obtained a loan for the remaining amount to be paid with monthly installments over the next $30$ years $(360$ monthly payments$).$ The interest rate is $9\%$ per year, compounded monthly. Answer the following question.

After $10$ years $($i$.$e$.$ after making $120$ payments$),$ the company decided to pay the remain on the loan. What is the amount to be paid at the end of year $10$ to pay off the equivalent remaining payments?

a$.$ $$447,359$

b$.$ $$360,480$

c$.$ $$357,887$

d$.$ $$296,05$