| *4.2.8 Using Table 4.2, show that the bond payments can be regarded as payments on two separate loans. The first loan is of amount F with interest only at rate j (per coupon period) for n periods, plus return of F at the end of n periods. The second loan is an amorti- zation of P-F over n periods at effective rate j (per coupon pe- riod), with payments of F(r-j) per coupon period. This second loan is the amortization of premium if P>F. TABLE 4.2 Outstanding Balance Pay- K Principal Interest Due (Book Value ment Repaid after Payment) 0 P=F[1+(r-j).am] 1 F[1+(r-j). Fr F[j+(r-j)(1-v;)] F(r-j).v) 2 F[1+(r-j).an-2] Fr F[j+(r-j)(1V;-))] F(r-j).vn : : : k F[1+(r-j).On-] Fr F[j+(r-j)(1-v*-*+)) F(r-j). v;=k+1 : : : : F[1+(r-j).a) Fr F[j+(r-j)(1-v})] F(r-j).v} Fr+F F[j+(r-j)(1-v;)] F[1+(r-j).v;] n-1 n 0 | *4.2.8 Using Table 4.2, show that the bond payments can be regarded as payments on two separate loans. The first loan is of amount F with interest only at rate j (per coupon period) for n periods, plus return of F at the end of n periods. The second loan is an amorti- zation of P-F over n periods at effective rate j (per coupon pe- riod), with payments of F(r-j) per coupon period. This second loan is the amortization of premium if P>F. TABLE 4.2 Outstanding Balance Pay- K Principal Interest Due (Book Value ment Repaid after Payment) 0 P=F[1+(r-j).am] 1 F[1+(r-j). Fr F[j+(r-j)(1-v;)] F(r-j).v) 2 F[1+(r-j).an-2] Fr F[j+(r-j)(1V;-))] F(r-j).vn : : : k F[1+(r-j).On-] Fr F[j+(r-j)(1-v*-*+)) F(r-j). v;=k+1 : : : : F[1+(r-j).a) Fr F[j+(r-j)(1-v})] F(r-j).v} Fr+F F[j+(r-j)(1-v;)] F[1+(r-j).v;] n-1 n 0