A financial institution has the following market value balance sheet structure:

Assets Liabilities and Equity

Cash $$3,500$ Certificate of deposit $$50,000$

Bond $$50,000$ Equity $$3,500$

Total assets $$53,500$ Total liabilities and equity $$53,500$

$(1)$ The bond has a $10-$year maturity, a fixed$-$rate coupon of $10\%$ paid at the end of each year, and a par value of $$50,000.$ The certificate of deposit has a $1-$year maturity and an $8\%$ rate of interest. The FI expects no additional asset growth. What will be the net interest income at the end of the first year?

$(2)$ If at the end of year $1$ market interest rates have increased $100$ basis points $(1\%),$ what will be the net interest income for the second year? Is this result caused by reinvestment risk or refinancing risk?

$(3)$ Assuming that market interest rates increase $1\%,$ what will be the value of the bond at the end of year $1?$ What will be the market value of the equity for the FI$?$

$(4)$ If market interest rates had decreased $100$ basis points by the end of year $1,$ what will be the value of the bond at the end of year $1?$ What will be the market value of the equity for the FI$?$