HW1_Solutions.2006

HW1_Solutions.2006 - MS&E 242 Investment Science Prof....

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MS&E 242 Investment Science HW #1 Solutions Prof. James Primbs October 3, 2006 Problem 2.1 (a) $1(1.033) (2006-1776) = 1,750.14 (Hence closest to $1,000) (b) $1(1.066) (2006-1776) = 2,421,900 (Hence closest to $1,000,000) Problem 2.2 We need to solve the equation for n. Taking logarithm of both sides and dividing by n gives: 2 ) 1 ( = + n r n n r 69 . 0 ) 2 ln( ) 1 ln( = = + . 1) Using the approximation ln(1 ) rr + leads to 0.69 69 69 100 rn nr =⇒ == i . 2) Using the approximation 2 2 1 ) 1 ln( r r r + leads to n r r r 69 . 0 ) 1 ln( 2 2 1 = + or n r r 69 . 0 ) 1 ( 2 1 . Now plugging in r = 0.08 for the term in parenthesis gives n r 69 . 0 ) 96 . 0 ( = or n r 72 . 0 = . This is the rule of 72, we only need to convert r to a percent ( i = 100r ). So, in terms of i : n i 72 = . Problem 2.3 (a) 12 12 03 . 0 ) 1 ( ) 1 ( + = + r so % 04 . 3 = r (b) 12 12 18 . 0 ) 1 ( ) 1 ( + = + r so % 56 . 19 = r (c) 4 4 18 . 0 ) 1 ( ) 1 ( + = + r so % 25 . 19 = r Problem 2.9 In this problem, we just need to compute the present values of the the cash flow streams assuming no roof, and assuming the current roof lasts for 5 years. The value of the roof is the difference between these present values.
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HW1_Solutions.2006 - MS&E 242 Investment Science Prof....

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