Question

Saved Both Bond Sam and Bond Dave have 7.3 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has three years to maturity, whereas Bond Dave has 20 years to maturity. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam and Bond Dave? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Percentage change in price of Bond Sam Percentage change in price of Bond Dave % If rates were to suddenly fall by 2 percent instead, what would be the percentage change in the price of Bond Sam and Bond Dave? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) % Percentage change in price of Bond Sam Percentage change in price of Bond Dave %

Answer 1

Assume par value of bond = $1000

Since it is semi-annually paid so coupon amount becomes half and time period become double taking current price of the bond $1000.So 7.3% of 1000=73.half of 73/2=36.5.

A: When interest rate increase by 2%,

Therefore 7.3% becomes 9.3%, so half of 9.3% is 4.65% or 0.0465

New Price of bond sam = 36.5*(1-1.0465^-6)/0.0465 + 1000/1.0465^6

                                    = 187.3546 + 761.3154

                                    = 948.67

Percentage change in price of Bond Sam = (948.67-1000)/1000 *100 = -5.133% = -5.13%

New Price of bond sam = 36.5*(1-1.0465^-40)/0.0465 + 1000/1.0465^40

                                    = 657.5166 + 162.3419

                                    = 819.8585

Percentage change in price of Bond Dave = (819.8585-1000)/1000 *100 = -18.0142% = -18.01%

B: When interest rate decrease by 2%,

therefore 7.3% becomes 5.3%, so half of 5.3% is 2.65% or 0.0265

New Price of bond sam = 36.5*(1-1.0265^-6)/0.0265 + 1000/1.0265^6

                                    = 200.0419 + 854.7641

                                    = 1054.806

Percentage change in price of Bond Sam = (1054.806-1000)/1000 *100 = 5.4806% = 5.48%

New Price of bond sam = 36.5*(1-1.0265^-40)/0.026 + 1000/1.0265^40

                                    = 893.5329 + 351.2706

                                    = 1244.804

Percentage change in price of Bond Dave = (1244.804-1000)/1000 *100 = 24.48035% = 24.48%

All green highlighted numbers are answers to the problem