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Chapter009

Chapter009 - The Theory of Interest Solutions Manual...

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The Theory of Interest - Solutions Manual 104 Chapter 9 1. A: A direct application of formula (9.7) for an investment of X gives ( ) ( ) 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 ( ) 10 1.028571 1.32539 . B X X = = The ratio / 1.00. A B = 2. Proceeding similarly to Exercise 1 above: ( ) 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 ( ) ( ) 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 ( ) ( ) 2 15 15 .032 1 1 1 18,000 1.032 1.032 1.032 18,000 \$211,807 to the nearest dollar. a + + + = = " 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 ′ = = = + +

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