Question

Please answer it in 1 hour Write explanation if it needed I’ll give you upvote immediately Don’t use excel to solve this question i In a bond amortization schedule, what does the book value mean?Describe in words. (ii) Consider a n-period coupon bond where the redemption amount, C may not be the same as the face amount, F. Using j and g to represent the yield rate per period and modified coupon rate per period respectively, show that,for k = 01,2,n, the book value at time k,B is B=C+Cg-jan-kj and the amortized amount at time k is ii Let K = Cu. The Makeham formula to compute the price of a bond is given by A verbal interpretation for K would be that K is the present value of the redemption value C.Provide a verbal interpretation for(C-K)

Answer 1

(i) In a bond amortization schedule, the book value represents the remaining amount of the bond principal that hasn't been paid off at a given point in time. When a bond is first issued, its book value equals its face value. As payments are made over the life of the bond, a portion of these payments reduces the book value. By the end of the bond's life, its book value will be zero, as the entire principal will have been paid off.

(ii) The formula for the book value B at time k, where k is the number of periods elapsed, is B = C + Cg - jan-kj.

Here:

- C is the redemption amount,

- g is the modified coupon rate per period,

- j is the yield rate per period, and

- a_n-kj is the present value of an annuity immediate with n - k periods at the yield rate j.

This formula states that the book value at any time k is the redemption amount plus the present value of the future coupon payments (Cg), minus the present value of the annuity that represents the repayments of the bond (jan-kj).

The amortized amount at time k is the change in the book value from time k-1 to time k, plus the coupon payment at time k. It represents the portion of the bond's principal (and interest) that has been repaid up to time k.

(iii) If K is defined as the present value of the redemption value C, according to the Makeham formula, (C-K) would represent the difference between the redemption value of the bond and its present value. This difference is the amount of interest that will accumulate over the life of the bond. In other words, (C-K) can be interpreted as the total interest that the bondholder will earn from holding the bond until redemption, assuming that all coupon payments are reinvested at the yield rate j.

Step-by-step explanation: