This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ACF329 Interest Theory Fall 2010 University of Texas at Austin HW 3  Solutions Instructor: Milica Cudina 3.7.2. We split the annuitydue from the problem into two annuitiesdue: one with payments of 100 and the other with payments of 300. The latter annuity is one halfyear deferred. With i = 0 . 06, the present value of Suzannes annuitydue can then be calculated as 100 a 20 i + (1 + i ) 1 / 2 300 a 20 i = 100 a 20 i (1 + 3(1 + i ) 1 / 2 ) 100 12 . 158 3 . 914 4 , 758 . 51 . 3.7.4 Let P = 100, i 1 = 0 . 15 and i 2 = 0 . 06. Then, the accumulated value of Bills deposits at the end of 13 years equals P ( s 5 i 1 (1 + i 2 ) 8 + s 8 i 2 ) = P 1 . 15 5 1 . 15 (1 . 06) 8 + 1 . 06 8 1 . 06 = 20 . 4638 P. On the other hand, Seths deposits must satisfy 20 . 4638 P = P s 13 i = P (1 + i ) 13 1 i . Using our calculator, we solve for i , we get i . 0738. 3.7.6 The present value of the annuity X is PV ( X ) = 1000 a 12 + 2000 v 12 a 18 with v = 1 d = 0 . 9. So, PV ( X ) = 1 . 1111(6458 . 475 + 4320 . 98553) = 1 . 1111 10779 . 4605 = 11977 . 0586 .. The present value of the perpetuity Y can be expressed as PV ( Y ) = Qa 20 + 3 Qv 20 a = Q ( a 20 + 3 v 20 a ) = Q (7 . 9064 + 3 . 9 20 / . 1111 = 11 . 1893 Q....
View
Full
Document
This note was uploaded on 12/05/2011 for the course M 341 taught by Professor Hietmann during the Spring '08 term at University of Texas at Austin.
 Spring '08
 HIETMANN

Click to edit the document details