Krzys’ Ostaszewski, http://www.math.ilstu.edu/krzysio/, Exercise 169, 8/9/8 Author of a study manual for exam FM available at: http://smartURL.it/krzysioFM (paper) or http://smartURL.it/krzysioFMe (electronic) Instructor for online seminar for exam FM: http://smartURL.it/onlineactuary If you find these exercises valuable, please consider buying the manual or attending our seminar, and if you can’t, please consider making a donation to the Actuarial Program at Illinois State University: https://www.math.ilstu.edu/actuary/giving/ Donations will be used for scholarships for actuarial students. Donations are taxdeductible to the extent allowed by law. Questions about these exercises? E-mail: [email protected] Study Note FM-09-05, Problem No. 50 A 1000 bond with semi-annual coupons at i ( 2 ) = 6% matures at par on October 15, 2020. The bond is purchased on June 28, 2005 to yield the investor i ( 2 ) = 7%. What is the purchase price? Assume simple interest between bond coupon dates, and the following day count: Date Day of the Year April 15 105 June 28 179 October 15 288 A. 906 B. 907 C. 908 D. 919 E. 925 Solution. We start by finding the price of the bond on the previous coupon date: April 15, 2005. On that date, there are 31 coupons of $30 each left and the price is: 31 30 ⋅ a31 3.5% + 1000v3.5% ≈ 906.32. Therefore, the price on June 28 is (note the use of simple interest for interim accumulation) 74 ⎛ 179 − 105 ⎞ ⎛ ⎞ 906.32 ⋅ ⎜ 1 + ⋅ 0.035 ⎟ = 906.32 ⋅ ⎜ 1 + ⋅ 0.035 ⎟ ≈ 919.18. ⎝ ⎠ ⎝ 182.5 ⎠ 182.5 This is a form of the flat price, not market price, and the reason why we use the flat price is that the question asks for the purchase price. Answer D. © Copyright 2006-2008 by Krzysztof Ostaszewski. All rights reserved. Reproduction in whole or in part without express written permission from the author is strictly prohibited. Exercises from the past actuarial examinations are copyrighted by the Society of Actuaries and/or Casualty Actuarial Society and are used here with permission.