HW2 Solution - PV = A r 1-1 (1 + r ) n = $8882 . 74 . 08...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
MIE375H1F - Financial Engineering - HW2 Solutions Nick Yeung September 29, 2010 Question 3.3 3.3a E [ age ] = 101 X x =90 p x · x = 0 . 07(90) + 0 . 08(91) + ... + 0 . 04(101) = 95 . 13 3.3b Since the expected age is not an integer, we can take a weighted average of an annuity up to age 95 and one up to age 96: PV 95 = 10000 0 . 08 h 1 - 1 (1 + 0 . 08) 5 i = $39 , 927 . 10 PV 96 = 10000 0 . 08 h 1 - 1 (1 + 0 . 08) 6 i = $46 , 228 . 80 PV 95 . 13 = 0 . 87 PV 95 + 0 . 13 PV 96 = 0 . 87($39927 . 10) + 0 . 13($46228 . 80) = $40746 . 32 3.3c Given age x , the annuity is: PV x = 10000 0 . 08 h 1 - 1 (1+0 . 08) ( x - 90) i , therefore, the expected annuity is: E [ annuity ] = 101 X x =90 p x · PV x = 101 X x =90 p x · 10000 0 . 08 h 1 - 1 (1 + 0 . 08) ( x - 90) i = $38 , 387 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Question 3.5 Since the call is advantageous, it means that the face value +5% is worth less than the future cash flows given the new yield, y . Hence, assuming annual coupons: 105 100 (1 + y ) 15 + 10 y ± 1 - 1 (1 + y ) 15 ² The above polynomial can be solved using a computer to yield y 9 . 366% Question 3.8 In this mortgage, P = $100 , 000, n = 30 years, r = 8%. 3.8a A = r (1 + r ) n P (1 + r ) n - 1 = (0 . 08)(1 . 08) 30 ($100000) (1 + 0 . 08) 30 - 1 = $8882 . 74 3.8b The mortgage balance after 5 years can be seen as the PV of the next 25 year’s payments
Background image of page 2
Background image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PV = A r 1-1 (1 + r ) n = $8882 . 74 . 08 1-1 (1 + 0 . 08) 25 = $94821 . 26 3.8c Using the new Principal from 3.8b and the new r = 9% and new term of 25 years: A = r (1 + r ) n P (1 + r ) n-1 = (0 . 09)(1 + 0 . 09) 25 ($94 , 821 . 26) (1 + 0 . 09) 25-1 = $9653 . 40 2 3.8d Solving for n : 8882 . 74 = (0 . 09)(1 + 0 . 09) n ($94 , 821 . 26) (1 + 0 . 09) n-1 n = 37 . 6 years It will take another 37.6 years before the mortgage is paid o for a total of 42.6 years on the mortgage. Question 3.9 Assuming semi-annual coupons, n = 36, r = 4 . 5%, Face Value of $100, Coupon Payments = $4 Price = C r 1-1 (1 + r ) n + F (1 + r ) n = 4 . 045 1-1 (1 + 0 . 045) 36 + 100 (1 + 0 . 045) 36 = 91 . 17 3...
View Full Document

This note was uploaded on 04/20/2011 for the course MIE 375 taught by Professor R.kwon during the Spring '11 term at University of Toronto- Toronto.

Page1 / 3

HW2 Solution - PV = A r 1-1 (1 + r ) n = $8882 . 74 . 08...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online