Question

Please see the two pics, one is the question and other one is the formula, please show me the steps

currently A coupon bond that has a $1,000 par value and a coupon rate of 10%. The bond is selling for $1,250 and has eight years to maturity. What is the bond's yield to maturity? (An equation is sufficient.) 3,

Answer 1

Maturity = 8 Years (n)
Price = 1250(P)
Par Value = 1000(F)
Coupon = Coupon Rate* Par Value = 10%*1000 = 100(C)

P = C/(1+i) + C/(1+i)² + C/(1+i)³ + ....... + 1000/(1+i)¹⁰
1250 = 100/(1+i) + 100/(1+i)² + 100/(1+i)³ ......+ 1000/(1+i)¹⁰
1250 = 1000(1-(1+i)^-10)/i + 1000/(1+i)¹⁰ (Sum of Coupons using PV of annuity formula)

Hit and Trial Method
Applying i =9% , We get RHS value = 1064.18
i = 8% , We Get RHS value = 1134.20
i = 7% , We Get RHS value = 1210.71
i= 6% We get RHS = 1294.50
I = 6.5% We get RHS = 1251.61
AT i = 6.52% We get RHS = 1250

Hence YTM = 6.52%

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