Answer: 9.685 years (approximately 9.7years)
the bond would take 9.685 years to mature
Explanation:
Using yield to maturity formula
YTM = C + (fv - pv) /n ÷ (fv + pv) /2
C = coupon rate = 7% of par value
= (7/100)× 1000
= $70
Fv = face value (par value) = $1,000
Pv = price = $1,020.46
YTM = yield to maturity = 0.0672
n = number of years to maturity..?
Using the above formula ;
0.0672= 70 + (1000-1020.46)/n ÷ (1000+1020.46)/2
0.0672= 70 + (-20.46)/n ÷ (2020.46)/2
0.0672= 70 + (-20.46)/n ÷ 1010.23
70 - (20.46)/n = 0.0672 × 1010.23
70 - (20.46)/n = 67.887456
-20.46 / n = 67.887456 - 70
-20.46 / n = - 2.112544 ( Cross multiply
-20.46 = - 2.112544n
Divide both sides by - 2.112544
n = 9.6850
The number of years for the bond to mature is 9.685 years (approximately 9.7years)
