Corporate bond A has a 6 percent coupon and matures in 3 years. Corporate bond B has a 6 percent coupon and matures in 15 years. The current interest rate is 6 percent. By how much will Bond A and Bond B change in price if the market rate increases to 6.5 percent

New price of bond A = $986.76, this means that the price decreased by $13.24 or 1.32%.

New price of bond B = $952.99, this means that the price decreased by $47.01 or 4.7%.

Explanation:

Since the current market interest is 6%, then both coupons A and B are sold at face value. If the market interest increases to 6.5%, then

New price of bond A:

PV of face value = $1,000 / (1 + 6.5%)³ = $827.85

PV of coupon payments = $60 x 2.64848 (PV annuity factor, 6.5%, 3 periods) = $158.91

New price of bond A = $986.76, this means that the price decreased by $13.24 or 1.32%.

New price of bond B:

PV of face value = $1,000 / (1 + 6.5%)¹⁵ = $388.83

PV of coupon payments = $60 x 9.40267 (PV annuity factor, 6.5%, 3 periods) = $564.16

New price of bond B = $952.99, this means that the price decreased by $47.01 or 4.7%.

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