Consider a bond with face value $$1000$ paying a coupon rate of $20\%$ per year quarterly when the market interest rate is only $4\%$ per year. The bond has three years until maturity. $($Please write the mathematical formula by which you will get a solution of Bond Price but you can solve it by using a financial calculator or Excel Calculator.$)$

a$.$ a$.$ Find the bond's price today and six months from now after the next coupon is paid.

b$.$ What is the total rate of return on the bond at six months from now after the next two coupons are paid? $($Suppose the coupons is not reinvested$)$