Question

6. A bond with par value of $1000, coupon rate of 10%, is now selling for $1,079.85, yield to maturity for this bond is 8%. Calculate the maturity of this bond?

Note; I want the answer with traditional formula and steps

Answer 1

Let the bond maturity be n years

Coupon amount =$1000 *10% = $100 per year

So, for n years $100 was received and after n years $1000 was received by Bondholder and the price paid was $1079.85 and the YTM was 8%

So, using the bond pricing formula, PV of all payments is equal to price

100/1.08+100/1.08^2+...+100/1.08^n +1000/1.08^n = 1079.85

100/0.08*(1-1/1.08^n)+1000/1.08^n = 1079.85

=> 1250 -1250/1.08^n +1000/1.08^n = 1079.85

=> 1250-250/1.08^n=1079.85

=> 250/1.08^n = 170.15

=> 1.08^n = 1.469292

Taking natural log of both sides

n*ln(1.08) = ln(1.469292)

=> n = ln(1.469292)/ln(1.08) = 4.999679 or 5

So, the maturity of the bond is 5 years