Chapter010

# Chapter010 - The Theory of Interest - Solutions Manual...

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The Theory of Interest - Solutions Manual 117 Chapter 10 1. ( a ) We have ( ) () ( ) ( ) 123 4 5 1000 1.095 1.0925 1.0875 1.08 1.07 \$3976.61. −−− ⎡⎤ +++ + = ⎣⎦ ( b ) The present value is greater than in Example 10.1 (1), since the lower spot rates apply over longer periods while the higher spot rates apply over shorter periods. 2. We have 234 1234 23 4 1000 1 1.05 1 1.05 1 1.05 1 1.05 1 1.05 1.05 1.05 1.05 1000 1 \$4786.78. 1.09 1.081 1.0729 1.06561 ssss −−−− + + ++ ⎛⎞ =+ + + + = ⎢⎥ ⎜⎟ ⎝⎠ 3. Since k s is differentiable over 04 , k .002 .001 0 at 2 k d sk k dk = −= = which is a relative maximum or minimum. Computing values for 0,1,2,3,4 k = we obtain 01 2 3 4 .09 .0915 .092 .0915 .09. ss s s s == = = = ( a ) Normal. ( b ) Inverted. 4. Payment at Spot rate Accumulated value 0 t = .095 5 1.095 1.57424 = 1 t = .0925 .0025 4 1.09 1.41158 = 2 t = .0875 .0050 3 1.0825 1.26848 = 3 t = .0800 .0075 2 1.0725 1.15026 = 4 t = .0700 .0100 1 1.06 1.06000 = 6.4646

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The Theory of Interest - Solutions Manual Chapter 10 118 5. Adapting Section 9.4 to fit this situation we have () 4 22 10,000 1.0925 \$11,946.50. 1.05 1.04 = 6. ( a ) ( ) 2 2 930.49 1019.31 \$841.67. BA PP −= = ( b ) ( ) 2 2 1000.00 1000.00 \$1000.00. CC = ( c ) We have 2 .09 s = and 2 841.67 1.09 1000.00 confirming the statement. = 7. The price of the 6% bond per 100 is 6 .06 6.12 6 100 1.12 75.33. Pa =+ = The price of the 10% bond per 100 is 6 .10 6.08 10 100 1.08 109.25. = We can adapt the technique used above in Exercise 6. If we buy 10/6 of the 6% bonds, the coupons will exactly match those of the 10% bond. The cost will be 10 10 75.33 125.55 and will mature for 100 . 66 = Thus, we have 6 6 4 125.55 109.25 1 100 6 s −+ = and solving 6 .2645, s = or 26.45%. 8. Applying formula (10.4) ( a ) 2 12 11 . 0 8 .0796, or 7.96%. 1.07 1.08 −− = + ( b ) ()() 3 123 . 0 9 .0888, or 8.88%. 1.07 1.08 1.09 −−− = ++ ( c ) The yield curve has a positive slope, so that the at-par yield rate increases with t .
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## This note was uploaded on 11/18/2010 for the course MATH 320 taught by Professor Dr.k during the Spring '10 term at Nevada.

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Chapter010 - The Theory of Interest - Solutions Manual...

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