Question

i think i should use the same n to calculate the yield but it is too hard to do the calculation

(1 point) An investor purchases two bonds with the following properties Bond 1: Has a face value $1000 and is redeemable at par. Pays coupons annually at a rate of 7.2% annual and was purchased for $1177.69 Bond 2: Has a face value $1000 and is redeemable at par. Pays coupons annually at a rate of 5.9% annual and was purchased for $1084.17. If both bonds mature in the same number of years and the investor yields the same rate on both bonds, find the yield rate (as a percent correct to 2 decimal places) Answer:

Answer 1

Yield To Maturity(YTM) = (interest per period+ ((Redemption price - Current market price) / life remaining to maturity)) / ((.4*Redemption price)+ (.6*Current market price))

Let n be the life remaining to maturity.

YTM of Bond 1 = YTM of Bond 2

((1000*7.2%)+((1000-1177.69)/n)) / (.4*1000+.6*1177.69) = ((1000*5.9%)+((1000-1084.17)/n)) / (.4*1000+.6*1084.17)

(72+((-177.69)/n)) / 1106.614 = (59)+((-84.17)/n)) / 1050.502

(72+((-177.69)/n)) * 1050.502 = (59)+((-84.17)/n)) *1106.614

75636.144-(186663.70038/n) = 65290.226-(93143.70038/n)

186663.70038/n - 93143.70038/n = 75636.144 - 65290.226

93520/n = 10345.918

n = 93520/10345.918

= 9.03931386272

life remaining to maturity = 9

Put the value of n to any of the equation

YTM = (59)+((-84.17)/n)) / 1050.502

= (59)+((-84.17)/9)) / 1050.502

= (59-9.35222222222) / 1050.502

= 49.6477777778/1050.502

= 0.04726100262

= 4.73%