The yield to maturity of a $1 000 bond with a 6.6% coupon​ rate, semi-annual​ coupons, and two years to maturity is 8.2% APR​, compounded​ semi-annually. What must its price​ be?

To calculate the price of the bond, we need to calculate the present value of the bond's cash flows, which are the coupon payments and the face value.

1. First, we need to calculate the semi-annual coupon payment. The bond has a 6.6% coupon rate, so the annual coupon payment is 6.6% of $1,000, which is$66. Since the bond pays coupons semi-annually, the semi-annual coupon payment is $66/2 =$33.

2. Next, we need to calculate the present value of the coupon payments. The bond pays $33 every six months for two years, which is a total of 4 payments. The yield to maturity is 8.2% APR compounded semi-annually, so the semi-annual discount rate is 8.2%/2 = 4.1%.

3. The present value of the coupon payments is $33/(1+4.1$33/(1+4.1%)^2 + $33/(1+4.1$33/(1+4.1%)^4 = $31.71 +$30.47 + $29.27 +$28.11 = $119.56.

4. We also need to calculate the present value of the face value, which is the amount the bondholder receives at maturity. The face value is $1,000, and it is discounted back to the present at the semi-annual discount rate for 4 periods. The present value of the face value is$1,000/(1+4.1%)^4 = $885.30.

5. Finally, we add the present value of the coupon payments and the present value of the face value to get the price of the bond. The price of the bond is $119.56 +$885.30 = $1,004.86.

So, the price of the bond must be approximately $1,004.86.