**Problems 6**–**Problems 10**–**Problems 22**–**Problems 30**–**Bank 1**has assets composed solely of a 10-year, 12 percent coupon, $1 million loan with a 12 percent yield to maturity. It is financed with a 10-year, 10 percent coupon, $1 million CD with a 10 percent yield to maturity.**Bank 2**has assets composed solely of a 7-year, 12 percent, zero-coupon bond with a current value of $894,006.20 and a maturity value of $1,976,362.88. It is financed by a 10-year, 8.275 percent coupon, $1,000,000 face value CD with a yield to maturity of 10 percent.

- If interest rates rise by 1 percent (100 basis points), how do the values of the assets and liabilities of each bank change?
- What accounts for the differences between the two banks’ accounts?

**Problems 32 –**What is the duration of a five-year, $1,000 Treasury bond with a 10 percent semiannual coupon selling at par? Selling with a yield to maturity of 12 percent? 14 percent? What can you conclude about the relationship between duration and yield to maturity? Plot the relationship. Why does this relationship exist?

**SOLUTION **

What is the duration of a five-year, $1,000 Treasury bond with a 10 percent semiannual coupon selling at par? Selling with a yield to maturity of 12 percent? 14 percent? What can you conclude about the relationship between duration and yield to maturity? Plot the relationship. Why does this relationship exist?

__Five-year Treasury Bond:__

Par value = $1,000, Coupon rate = 10%, Semiannual payments, R = 10%, Maturity = 5 years

__ t __ __CF____t__ __ ____DF____t __ __CF____t ____x DF____t__ __CF____t ____x DF____t ____x t__

0.5 | 50 | 0.9524 | 47.620 | 23.810 |

1.0 | 50 | 0.9070 | 45.350 | 45.350 |

1.5 | 50 | 0.8638 | 43.190 | 64.785 |

2.0 | 50 | 0.8227 | 41.135 | 82.270 |

2.5 | 50 | 0.7835 | 39.175 | 97.937 |

3.0 | 50 | 0.7462 | 37.310 | 111.930 |

3.5 | 50 | 0.7107 | 35.535 | 124.373 |

4.0 | 50 | 0.6768 | 33.842 | 135.368 |

4.5 | 50 | 0.6446 | 32.230 | 145.035 |

5.0 | 1,050 | 0.6139 | 644.595 | 3,222.975 |

1,000.00 | 4,053.833 |

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