Question

Bond 1 has a maturity of 10 years, a coupon payment of $50/year, and a Face Value of $1,000. Bond 2 has a maturity of 5 years, a coupon payment of $50/year, and a Face Value of $1,000. Both bonds had initial coupon rates of 5%. If market interest rates for these two bonds increase to 6%, by how much will the longer maturity bond fall in price compared to the shorter maturity bond? This means you have to find the current price of each bond. Show your work.

Answer 1

Current price of bond 1 = 50(P/A, 6%, 10) + 1,000(P/F, 6%, 10)

                                      = 50(7.360) + 1,000(0.5584)

                                      = 368 + 558.4

                                      = $926.4

Current price of bond 2 = 50(P/A, 6%, 5) + 1,000(P/F, 6%, 5)

                                      = 50(4.212) + 1,000(0.7473)

                                      = 210.6 + 747.3

                                      = $957.9

The fall in price of the longer maturity bond compared to the shorter maturity bond = 957.9 - 926.4 = $31.50.