# 1. The yield to maturity of a bond with $1,000 par value, 7% coupon rate, semiannual coupons, and two years to maturity is 7.6% APR. Find its price.

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1. The yield to maturity of a bond with $1,000 par value, 7% coupon rate, semiannual coupons, and two years to maturity is 7.6% APR. Find its price.

2. A bond with an 8 year maturity, $5,000 face value, 4.4% coupon rate and semiannual payments is currently selling for a price of $4,723.70. Which of the following options repre- sents its yield to maturity?

a)2.675% b)4.4% c)5.25% d)10.5%

3. A three year zero-coupon bond has a face value of $100 and yield to maturity of 6.00%. Find its price.

4. One company has issued two types of bonds, X and Y. Both bonds have 10 years maturity, a face value of $100, make semiannual payments, and a yield to maturity of 5%. However, bond X has a coupon rate of 5% while for bond Y it is 15%. If interest rates suddenly rise by 2% (so the new yield to maturity of both bonds is 7%), which bond suffers the largest percentage change in its price? (Hint: compute the price of both bonds with the 5% YTM and then with 7% YTM, the compute the percentage change in price.)

5. Suppose we have a five-year bond with face value of $1000, a coupon rate of 7%, semi-annual coupon payments, and a yield to maturity of 5% APR. This bond allows the issuer to not make coupon payments for the first year. Find its price. (Hint: this is a two step problem. If we are at year 1, this is a regular four-year bond, find its price this way and then discount it back to year 0.)

6. On March 15, 2016, the U.S. government issued a bond with maturity of February 15, 2046, coupon rate of 2.5%, $100 in face value, and semiannual payments made on February 15 and August 15 of each year.

If the yield to maturity of this bond is 2.67%, what was its price on the day it was issued (March 15, 2016)? (Hint: find the PV of all payments as of August 15, 2016 and then discount it back to March 15.)