Question

Christie DeLeon purchased a ten-year $1,000 bond with semiannual coupons for $962. The bond had a $1,200 redemption payment at maturity, a nominal coupon rate of 7% for the first five years, and a nominal coupon rate of q% for the final five years. Christie calculated that her annual effective yield for the ten-year period was 7.25%. Find q. (Round your answer to two decimal places.)

Answer 1

Effctive Yield = [(1+Semi Annual Rate)^2]-1

0.0725 = [(1+R)^2]-1

1.0725^1/2 = 1+R

Therefore, R = 1.035616-1 = 0.035616

Period	Cash Flow	Discounting Factor [1/(1.035616^year)]	PV of Cash Flows (cash flows*discounting factor)
1	35	0.965608874	33.7963106
2	35	0.932400498	32.63401744
3	35	0.900334195	31.51169684
4	35	0.869370689	30.42797412
5	35	0.839472052	29.38152183
6	35	0.810601664	28.37105822
7	35	0.78272416	27.3953456
8	35	0.755805395	26.45318882
9	35	0.729812397	25.54343388
10	35	0.704713327	24.66496644
11		0.680477442	0
12		0.657075057	0
13		0.634477506	0
14		0.61265711	0
15		0.591587143	0
16		0.571241795	0
17		0.551596147	0
18		0.532626134	0
19		0.514308522	0
20		0.496620873	0
20	1200	0.496620873	595.9450475
		Price of the Bond = Sum of PVs	886.1245613

Price of Bond without considering coupons for last 5 years = 886.12

PV of Coupons of last 5 years = 962-886.12 = $75.88

FV of $75.88 at the end of 5th year = PV*[(1+Interest Rate)^Number of Periods] = 75.88*[(1+0.035616)^10] = 75.88*1.419 = $107.67

PV of Annuity = P*[1-{(1+i)^-n}]/i

Where, PV = 107.67, i = Interest Rate = 0.035616, n = Number of Periods = 10

Therefore,

107.67 = P*[1-{(1+0.035616)^-10}]/0.035616

3.83477 = P*0.295287

Therefore, Coupon = Annuity = P = 3.83477/0.295287 = $12.9866

Therefore, Semi-Annual Rate = 12.9866/1000 = 0.0129866

Therefore, Nominal Annual Rate = Semi Annual Rate*2 = 0.0129866*2 = 0.0259732

Therefore, Q = 2.5973%