I'm required to calculate the yield to maturity for the following question:
An insurance company has invested in the following fixed-income security: $5,800,000 of 10-year bonds paying 7% interest with a par value of $6,000,000.
What I've done so far:
I've used the bond pricing formula -->
PV = A [(1 + (1+r)^-n)/r] + [FV/(1+r)^n]
where A = coupon payment, r =yield to maturity (YTM), FV = face value of bond, n = number of periods
I'm told that for the 10-year bonds: Par = $6,000,000; PV = $5,800,000, coupon = 7%
My equation so far:
5,800,000 = (6,000,000 x 0.07)*[ (1 - (1+r)^-10) / r] + [6,000,000 / (1+r)^10]
5,800,000 = 420,000[ (1 - (1+r)^-10) / r] + [6,000,000 / (1+r)^10]
Multiply both sides by [r(1+r)^10]
5,800,000r(1+r)^10 = 420,000((1+r)^10) [1 - (1+r)^-10)] + 6,000,000r 5,800,000r(1+r)^10 = 420,000((1+r)^10) + 420,000 + 6,000,000r
line is where I'm stuck.
I'm not sure where to go after that to solve for r.
Any help on solving r would be much appreciated
Thank you in advance.