a question for prof broverman regarding one of his posts.

[audia4]

I was working on the question of WEEk OF FEBRUARY 20/06.

The question was: An n year bond has face and redemption amount 100. The bond has level semiannual coupons and the yield rate is a nominal annual rate of 6% compounded semiannually. The bond's amortized value just after the 8th coupon is 121.13 and just after the 10th coupon it is 120.39. Find the original price of the bond.

my solution

OB_10 = OB_8(1+i)^2 -100(r)s_2, then using the value for r, I used

0B_10= OB_1(1+i)^9 -frs_1. Is this correct??

[Sam Broverman]

Audia4,

The relationship you wrote down should have been
0B_10= OB_1(1+i)^9 -frs_9 .
But we are trying to find the original bond purchase price,
which is OB_0 , not OB_1 . OB_1 would be the book value
one coupon period after the bond was purchased.

[audia4]

HOw could I therefore use my approach to solve this problem?

thanks you.

[Sam Broverman]

From your approach (corrected version) you can find OB_1.
But we want to find OB_0, so then you could use the
relationship OB_0 (1+i) - Fr = OB_1 to find OB_0 from OB_1 .
Since we are trying to find OB_0, it is more efficient to go
directly to OB_0 rather than finding OB_1 and the OB_0 from OB_1.