Chapter012 - The Theory of Interest - Solutions Manual...

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The Theory of Interest - Solutions Manual Chapter 12 1. ( 29 [ ] ( 29 [ ] ( 29 1 1 1 1 1 E E 1 E 1 from independence 1 . n t t n t t n a n i i i - - = - = - = Π + = Π + = + 2. ( 29 [ ] ( 29 1 1 1 1 1 1 1 E E 1 E 1 from independence 1 . n t s n t s n t s t s n t n i t a i i i a - = = - = = - = = Σ Π + = Σ Π + = Σ + = 3. ( a ) ( 29 ( 29 [ ] Year 1: 8% given. Year 2: .5 .07 .09 .08, or 8%. Year 3: .25 .06 2 .08 .10 .08, or 8%. + = + + = ( b ) ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 2 2 Year 1: 0, no variance. Year 2: .5 .07 .08 .09 .08 .0001 .0001 .01. Year 3: .25 .06 .08 2 .08 .08 .10 .08 .0002 σ = = - + - = = = = - + - + - = .0002 .01 2 = = ( c ) ( 29 ( 29 ( 29 1000 1.08 1.09 1.10 $1294.92. = ( d ) ( 29 ( 29 ( 29 1000 1.08 1.07 1.06 $1224.94. = ( e ) ( 29 3 1000 1.08 $1259.71. = ( f ) ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 [ ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ] [ ] .25 1000 1.08 1.09 1.10 1.08 1.09 1.08 1.08 1.07 1.08 1.08 1.07 1.06 .25 1294.92 1271.38 1248.05 1224.94 $1259.82 + + + = + + + = 141
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The Theory of Interest Chapter 12 ( g ) ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 .25 1294.92 1259.82 1271.38 1259.82 1248.05 1259.82 1224.94 1259.82 2720.79 2720.79 52.16. σ = - + - + - + - = = = 4. ( a ) ( 29 ( 29 ( 29 .09 1 .07 .09 .07 1 1 1 E 1 .09 .07 1 1 ln 1 .925952. .09 .07 Then set 1 .925952 and solve .07997. t i dt t t i i - - + = - + = + = - + = = ( b ) We have ( 29 ( 29 3 1 3 1.07997 .79390. a - - = = (c) ( 29 ( 29 ( 29 .09 2 2 .07 .09 .07 1 1 1 E 1 .09 .07 1 1 1 .857412. .09 .07 1 Then set 1 .857412 and solve .16630. t i dt t t k k - - + = - + - = × = - + + = = ( d ) Applying formula (12.10), we have ( 29 [ ] ( 29 ( 29 3 6 1 Var 3 .857412 .925952 .0000549 a - = - = and the standard deviation is .0000549 .00735. = 5. ( b ) Applying formula (12.11), we have 3 3 3 .07997 E 2.5772. i a a a = = = ( d ) Applying formula (12.14), we have ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 1 2 3 3 3 3 2 1 2 1 2 2 Var .857412 .925952 2 .857412 2.2229 2.5772 2.5772 .857412 .925952 .857412 .925952 .005444 a a a a a a a k i i m m m a a a a m m m m + = - - - - + = - - - - = and the standard deviation is .005444 .0735. = 142
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The Theory of Interest Chapter 12 6. The random variable ( 29 2 / 2 t i will be normal with 3% μ = and .25%. σ = ( a ) Applying formula (12.1), we have ( 29 [ ] ( 29 4 E 100 4 100 1.03 112.55. a = = Applying formula (12.3), we have ( 29 ( 29 ( 29 ( 29 ( 29 { } ( 29 4 8 2 2 4 4 2 8 Var 100 10,000 1 2 1 10,000 1 2 .03 .03 .0025 1.03 119.828 a i i s i = + + + - + = + + + - = and the standard deviation is 119.828 10.95 = .
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Chapter012 - The Theory of Interest - Solutions Manual...

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