Chapter009

# Chapter009 - The Theory of Interest Solutions Manual...

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The Theory of Interest - Solutions Manual Chapter 9 1. A: A direct application of formula (9.7) for an investment of X gives ( 29 ( 29 10 10 10 1.08 1.08 1.32539 . 1.05 1.05 A X X X = = = B: A direct application of formula (9.3a) for the same investment of X gives 1.08 1 1.028571 1.05 i + = = and the accumulated value is ( 29 10 1.028571 1.32539 . B X X = = The ratio / 1.00. A B = 2. Proceeding similarly to Exercise 1 above: ( 29 10 .08 10 10 .028571 9.60496. 1.05 11.71402. s A B s = = = = The ratio / .82. A B = 3. Again applying formula (9.7) per dollar of investment ( 29 ( 29 5 5 1.07 .87087 1.10 = so that the loss of purchasing power over the five-year period is 1 .87087 .129, or 12.9%. - = 4. The question is asking for the summation of the “real” payments, which is ( 29 ( 29 2 15 15 .032 1 1 1 18,000 1.032 1.032 1.032 18,000 \$211,807 to the nearest dollar. a + + + = = L 5. The last annuity payment is made at time 18 t = and the nominal rate of interest is a level 6.3% over the entire period. The “real” rate over the last 12 years is .063 .012 .0504. 1 1 .012 i r i r - - ′ = = = + + 104

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The Theory of Interest - Solutions Manual Chapter 9 Thus, the answer is ( 29 ( 29 ( 29 ( 29 6 12 .0504 50 1.063 50 .693107 8.84329 \$306 to the nearest dollar. X a - = = = 6. The profitability index (PI) is computed using nominal rates of interest. From formula (9.3a) ( 29 ( 29 1 1.04 and 1.04 1.035 1 .0764. 1.035 i i + = = - = The profitability index is defined in formula (7.20) 8 .0764 2000 NPV PI 1.17. I 10,000 a = = = 7. ( a ) Coupon 1 = ( 29 ( 29 10,000 1.04 .05 \$520. = Coupon 2 = ( 29 ( 29 ( 29 10,000 1.04 1.05 .05 \$546. = Maturity value = ( 29 ( 29 10,000 1.04 1.05 \$10,920. = ( b ) Nominal yield: The equation of value is ( 29 ( 29 ( 29 1 2 10,500 520 1 546 10,920 1 0 i i - - - + + + + + = and solving the quadratic we obtain .0700, or 7.00%. Real yield: The equation of value is ( 29 ( 29 ( 29 1 2 10,500 500 1 500 10,000 1 0 i i - - - + + + + + = and solving the quadratic we obtain .0241, or 2.41%. 8. Bond A: Use a financial calculator and set N 5 PV 950 PMT 40 FV 1000 and CPT I 5.16%. = = - = = = Bond B: The coupons will constitute a geometric progression, so ( 29 ( 29 ( 29 2 5 5 5 5 1.05 1.05 1.05 40 1000 1.05 1.0516 1.0516 1.0516 1.0516 1.05 1 1.0516 40 1.05 992.416 \$1191.50 .0516 .05 P - = + + + + - = + = - L 105
The Theory of Interest - Solutions Manual Chapter 9 9. ( a ) The final salary in the 25 th year will have had 24 increases, so that we have ( 29 24 10,000 1.04 \$25,633 to the nearest dollar. = ( b ) The final five-year average salary is ( 29 ( 29 ( 29 20 21 24 10,000 1.04 1.04 1.04 \$23,736 to the nearest dollar. 5

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Chapter009 - The Theory of Interest Solutions Manual...

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