Question

Please use equation to solve

Write the equation for yield to maturity if you purchase a 6% $1000 coupon bond that pays interest every 3 months for $900 and matures in 1 year.  

Answer 1

ANSWER:

PV = $900

FV = $1,000

I = 6% PER YEAR OR 6% / 4 = 1.5% PER QUARTER.

Coupon price = coupon rate * fv = 1.5% * $1,000 = $15

n = 1 year or 4 quarters.

pv = coupon price(p/a,i,n) + fv(p/f,i,n)

900 = 15(p/a,i,4) + 1,000(p/f,i,4)

solving via trial and error we get that i is between 4% and 5% as at 4% the pv is $909.25 while at 5% it is 875.89 and solving further we get that i is 4.2727%

so the ytm is 4.2727% per quarter.