Question

Use the following information for problems 1, 2, 3, and 4: A non-callable $1,000 par- value bond matures in thirty years at par. The annual coupon rate is 5% with coupons payable annually. The bond was purchased at a price to yield an annual effective rate of 4%. 1. (1 point) Find the bond purchase price. 2. (1 point) Calculate the Macaulay duration and the modified duration for this bond. 3. (2 points) Suppose that the market interest rate increases to 4.5%. Calculate the price of the bond at 4.5% using the first-order Macaulay approximation, 4. (2 points) Suppose that the market interest rate increases to 4.5%. Calculate the price of the bond at 4.5% using the first-order modified approximation.

Answer 1

Please find the solution in the below images

Solution on rate = 5.1; C-54100 0 F = $1000, coupon rat na 30 - $50 4. HTH = YTM - (+ F - P n ftp 2 el 50+ 1000-P 30 Yol love t ) 4000 typ - 5043 ot 100o-p. 250 34

3(4000 typ) = 20(2500 - Po 12p+ 2op.= soooo – 12,000 P = $1187.57 Macaulay duration - Chat+) . (ltr)t + / n CA Citrit Ca 50 (2 ) ++.50(30) ( + 5062 5 12 + 4 tu city ) h ! 10917-6932 2 10917.6932. 337 -3214 50 L1-L) (1.04) 1.04 & 32.36

- Marcaulay modified duration duration It YTM 1 Where, f= coupon fequency 32.36 lo Berb + 31.11 approximation - First order. Macaulay n mac D lold p. llit, JAP) = it Prews Change in price where i.pl mo cese old interest rate pt mac. D 32.36 - 170.71 1187.5 ADP = ity.s. To

so, the new price is approximately » P+DP 1187.5+ (-170.71 ) Pnew $ 1016.79 6 approximation First order modified DP = - P. Mod D. Di I when : Pf. Mad P ase old. intenst rates. Dia i new - Cold (4.5 - 4)/100 - 0-5/100 op - (1187.5) (31.01) (0.5) – 184.71 So, the new price is approximately en Ptop & 1187.5+ (- 184.71). & $1.002.79