Interest Rate Sensitivity THIS IS THE SECOND TIME I AM POSTING THIS QUESTION. IT
ID: 2772933 • Letter: I
Question
Interest Rate Sensitivity
THIS IS THE SECOND TIME I AM POSTING THIS QUESTION. IT WAS NOT answered correctly first time.
Interest Rate Sensitivity--I have answers show all work formulas
A Bond trader purchased each of the following bonds at a yield to maturity of 8%. Immediatey after she purchased the bonds interest rates fell to 7%. What is the percentage change in the price of each bond after the decline in interest rates? Fill in the following table: (I have all the answers but must show ALL WORK/Formulas). Show Work!
Price at 8% Price at 7% Percentage Change
10 year, 10% annual coupon
10 year zero
5 year zero
30 year zero
$100 perpetuity
Show all Work and formulas
Answers are: 10 year 10% coupon = 6.75%
10 year zero = 9.75%
5 year zero = 4.76%
30 year zero = 32.19%
$100 perpetuity = 14.29%
SHOW ALL WORK ALL FORMULAS.
Explanation / Answer
Answer :-
Let Face Value = 1000 & compounding anually
Interest rate = 8% & 7%
a.) Year = 10 years
coupon rate = 10%
coupon value = 1000 * 10%
= 100
Price at 8% = coupon value * PVIFA at (r,n) + Face value * PVIF at (r,n)
= (100 * 6.71) + (1000 * .429)
= $ 1100
Price at 7% = coupon value * PVIFA at (r,n) + Face value * PVIF at (r,n)
= (100 * 7.024) + (1000 * .508)
= $ 1210.4
% Change = (1210.4 - 1100) / 1100
= 10.03%
b.) Year = 10 years
coupon rate = 0%
coupon value = 1000 * 0%
= 0
Price at 8% = Face value * PVIF at (r,n)
= (1000 * .429)
= $ 429
Price at 7% = Face value * PVIF at (r,n)
= (1000 * .508)
= $ 508
% Change = (508 - 429) / 429
= 18.41%
c.) Year = 5 years
coupon rate = 0%
coupon value = 1000 * 0%
= 0
Price at 8% = Face value * PVIF at (r,n)
= (1000 * .681)
= $ 681
Price at 7% = Face value * PVIF at (r,n)
= (1000 * .713)
= $ 713
% Change = (713 - 681) / 681
= 4.7%
d.) Year = 30 years
coupon rate = 0%
coupon value = 1000 * 0%
= 0
Price at 8% = Face value * PVIF at (r,n)
= (1000 * .099)
= $ 99
Price at 7% = Face value * PVIF at (r,n)
= (1000 * .131)
= $ 131
% Change = (131 - 99) / 99
= 32.32%
e.) Price at 8% = $ 100 / .08
= $ 1250
Price at 7% = $ 100 / .07
= $ 1428.57
% Change = (1428.57 - 1250) / 1250
= 14.29%
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