Question

A ten year, $10,000 bond is purchased after 5 years and 6 months. If the bond rate is 6.5% payable semi-annually and money is worth 4.5% compounded semi-annually, what is the purchase price of the bond? Question 2 (4 marks) Bond certificates of $5000 are issued at 3% payable quarterly and are redeemable at par in three years. If the bonds are sold to yield 5% compounded quarterly, what is the premium/discount? Question 3 (7 marks) A $5000, 4.81% bond with semi-annual coupons is redeemable at par in 10 years and is purchased at 98.7. What is the approximate yield rate?

Please provide help with these questions. thanks

Answer 1

Q1) Purchase price of bond = 10,806.57

Q2) Discount = 276.98

Q3) YTM = 4.972%

BASIS FOR THE SOLUTION

Q1)Calculation of purchase price of bond using Excel formula:

Time till maturity (Nper) after 5 years and 6 months = 4.5 years = 9 periods of six months

Face value of bond (FV) = 10,000

Coupon amount (PMT) = 10,000 x (6.5%/2) = 325

YTM (I/Y) = 4.5%/2 = 2.25%

Present value formula ==PV (rate, nper, pmt, [fv])

Hence, purchase price of bond (PV) = 10,806.57

Q2. Calculation of purchase price of bond using Excel formula:

Time till maturity (Nper) = 3 years x 4 = 12 quarters

Face value of bond (FV) = 5,000

Coupon amount (PMT) = 5,000 x (3%/4) = 37.5

YTM (I/Y) = 5%/4 = 1.25%

Present value formula = =PV (rate, nper, pmt, [fv])

Hence, price of bond (PV) = 4,723.02

Discount = Price of bond - Face value of bond = 4,723.02 - 5,000 = 276.98

Q3. Calculation of YTM :

Time till maturity (N) = 10 years x 2 = 20 periods of six months

Face value of bond (FV) = 5,000

Coupon amount (PMT) = 5,000 x (4.81%/2) = 120.25

Purchase price of bond (PV) = 5,000 x 98.7% = 4,935

Hence, YTM (I/Y) = 2.488% for 6 months

YTM = 2.488% x 2 = 4.972% (see the below image for calculation)

Market price YTM = Interest & [ Maturity Value - M [Maturity Value + Market price 2 120-25 + 5000 - 4935 [5000 + 4935] 2 120.25 +3.25 4967.5 2.486%. Semíanuelly 2,486x2 = 4,972% 15