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 XX X ⎛⎞ == = ⎜⎟ ⎝⎠ B: A direct application of formula (9.3a) for the same investment of X gives 1.08 11 . 0 2 8 5 7 1 1.05 i += = and the accumulated value is 10 1.028571 1.32539 . BX 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 Bs ±± 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 21 5 15 .032 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. . 0 1 2 ir i r =
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The Theory of Interest - Solutions Manual Chapter 9 105 Thus, the answer is () ( ) ( ) 6 12 .0504 50 1.063 50 .693107 8.84329 $306 to the nearest dollar. Xa = == 6. The profitability index (PI) is computed using nominal rates of interest. From formula (9.3a) ( ) 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 = ( )( ) 10,000 1.04 .05 $520. = Coupon 2 = ( ) 10,000 1.04 1.05 .05 $546. = Maturity value = ( ) 10,000 1.04 1.05 $10,920. = ( b ) Nominal yield: The equation of value is 12 10,500 520 1 546 10,920 1 0 ii −− −+ + + + + = and solving the quadratic we obtain .0700, or 7.00%. Real yield: The equation of value is 10,500 500 1 500 10,000 1 0 + + + + = 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 ( ) 25 55 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 ⎡⎤ ⎛⎞ ⎛⎞⎛⎞ =+ + + + ⎢⎥ ⎜⎟ ⎜⎟⎜⎟ ⎝⎠ ⎝⎠⎝⎠ ⎣⎦ = "
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The Theory of Interest - Solutions Manual Chapter 9 106 9. ( a ) The final salary in the 25 th year will have had 24 increases, so that we have () 24 10,000 1.04 $25,633 to the nearest dollar. = ( b ) The final five-year average salary is ()() 20 21 24 10,000 1.04 1.04 1.04 $23,736 to the nearest dollar. 5 ⎡⎤ ++ + = ⎣⎦ " ( c ) The career average salary is 22 4 10,000 1 1.04 1.04 1.04 $16,658 to the nearest dollar. 25 + + = " 10. The annual mortgage payment under option A is 10 .10 240,000 40,000 32,549.08. A R a == The annual mortgage payment under option B is 10 .08 240,000 40,000 29,805.90. B R a The value of the building in 10 years is 10 240,000 1.03 322,539.93. = Thus, the shared appreciation mortgage will result in a profit to Lender B ( ) .50 322,539.93 240,000 41,269.97. −= ( a ) The present value of payments under Option A is 10 .08 40,000 32,549.08 $258,407 to the nearest dollar. A PV a =+ = The present value of payments under Option B is 10 10 .08 40,000 29,805.90 41,269.97 1.08 $259,116 to the nearest dollar.
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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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Chapter009 - The Theory of Interest - Solutions Manual...

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