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Chapter006

# Chapter006 - The Theory of Interest Solutions Manual...

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The Theory of Interest - Solutions Manual Chapter 6 1. ( a ) ( 29 10 1000 1.10 \$385.54 P - = = . ( b ) ( 29 10 1000 1.09 \$422.41 P - = = . ( c ) The price increase percentage is 422.41 385.54 .0956, or 9.56%. 385.54 - = 2. The price is the present value of the accumulated value, so we have ( 29 20 10 .08 1000 1 1.1 \$844.77. 2 P - = + = 3. ( a ) The day counting method is actual/360. In 26 weeks there are 26 7 182 × = days. Using the simple discount method, we have 182 9600 10,000 1 and .0791, or 7.91%. 360 d d = - = ( b ) An equation of value with compound interest is ( 29 1 2 9600 10,000 1 and .0851, or 8.51% i i - = + = . 4. We have 100, 105, .05, 5/105, .04, 5/.04 125, F C r g i G = = = = = = = ( 29 20 105 1.04 47.921, K - = = and 20 n = . Basic: ( 29 ( 29 20 20 5 105 5 13.59031 105 .45639 \$115.87 P a v = + = + = . Premium/discount: ( 29 20 105 5 4.2 \$115.87 P a = + - = . Base amount: ( 29 ( 29 20 125 105 125 1.04 \$115.87 P - = + - = . Makeham: ( 29 ( 29 5 47.921 105 47.921 \$115.87 .04 105 P = + - = . 5. We apply the premium/discount formula to the first bond to obtain ( 29 1136.78 1000 1000 .025 .02 n a = + - 59

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The Theory of Interest - Solutions Manual Chapter 6 which can be solved to obtain 27.356 n a = . Now apply the premium/discount formula to the second bond to obtain ( 29 ( 29 1000 1000 .0125 .02 27.356 \$794.83. P = + - = 6. Since the present value of the redemption value is given, we will use Makeham’s formula. First, we find 45 .04. 1125 Fr g C = = = Now ( 29 ( 29 .04 225 1125 225 \$945. .05 g P K C K i = + - = + - = 7. Since , n K Cv = we have 450 1000 n v = and .45 n v = . Now we will apply the base amount formula ( 29 ( 29 1 n n n P G C G v G v Cv = + - = - + and substituting values ( 29 1110 1 .45 450 and \$1200. G G = - + = 8. The price of the 10-year bond is ( 29 20 20 .035 1000 1.035 50 1213.19 P a - = + = . The price of the 8-year bond is ( 29 16 16 .035 1.035 .03 1213.19 P F Fa - = + = and solving ( 29 ( 29 1213.19 \$1291 to the nearest dollar. .576706 .03 12.09412 F = = + 9. Since n is unknown, we should use an approach in which n only appears once. We will use the base amount formula. First, we have ( 29 1000 .06 1200 .05 Fr G i = = = and ( 29 1200 1000 1200 1200 200 . n n P v v = + - = - 60
The Theory of Interest - Solutions Manual Chapter 6 If we double the term of the bond we have ( 29 2 50 1200 1000 1200 1250 200 . n n P v v + = + - = - Thus we have a quadratic which reduces to 2 200 200 50 0 n n v v - + = or 2 4 4 1 0 n n v v - + = and factoring ( 29 2 2 1 0. n v - = Thus, .5 n v = and ( 29 1200 200 .5 \$1100 P = - = . 10. ( a ) The nominal yield is the annualized coupon rate of 8.40%. ( b ) Here we want the annualized modified coupon rate, so 42 2 2 2 8.00%. 1050

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Chapter006 - The Theory of Interest Solutions Manual...

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