$12.$ Suppose A$-$rated bonds were trading in the market at a YTM of $10\%$ on all maturities, and you bought an A$-$rated, $10-$year, $9\%$ coupon bond with face value of $$1,000$ and annual coupon payments. Suppose that immediately after you bought the bond the yield on such bonds dropped to $8\%$ on all maturities and remains there until you sold the bond at your horizon date at the end of four years.

a$.$ What price did you pay for the $10-$year, $9\%$ coupon bond?

b$.$ Show in a flow matrix the coupons you received on the bond and their values at your horizon date from reinvesting.

c$.$ What is the price of the original $10-$year bond at your horizon date?

d$.$ What is your horizon date value and total return?