Bond A is a $1,000,5\%$ semi$-$annual coupon bond with $12$ years to maturity.

L If you bought Bond A today at a yield of $3\%,$ what is your purchase price?

b$.$ One year later Bond A$\text{'}$s YTM has gone up to $4\%$ and you sell it immediately after receiving the coupon.

i$.$ What is your current yield?

ii$.$ What is your capital gains yield?

iii. Assume that you reinvest all coupons at $4\%$ compounded semi$-$annually. What is your total rate of return?