# Finding principal repaid on a bond coupon

I got this problem wrong, I don't really know what to do.

A 10% bond with semi-annual coupons and face 11,000 matures 4 years after issue. What is the amount of principal repaid in the 5th coupon, if the nominal annual yield rate is 8%, compounded semi-annually?

The equation I have for principal adjustment is $g-i[1+(g-i)* \frac{1-v^{n-t+1}}{i}]=(g-i)v^{n-t+1}$

$F=11,000, r=.1/2=.05, i=.08/2=.04, n=8, t=5, Fr=550,$

$C=F(1+i)=11,000*1.04=11,440, g=(F/C)(r)=(11,000/11,440)(.05)=.0480769231$

$550*(.0480769231-.04)* \frac{1}{1.04}^4=3.797303233$

However, this is super wrong. Anybody know what I did to mess it up?

## 1 Answer

The problem was g. g should have been equal to r, because F was supposed to be equal to C.

$P_{5}=C(g-i)v^4$

$11,000(.05-.04)*1.04^{-4} \approx 94.03$