Question

A 10-year bond with semi-annual coupons is bought at a discount to yield 9% convertible semiannually. If the amount for accumulation of discount in the next-to-last coupon is 8, nd the total amount for accumulation of discount during the rst four years in the bond amortization schedule.

Answer 1

Answer:

The answer is 33.98.

Explanation:

Discount the accumulation of discount in the 19th coupon 18 periods to find the accumulation of discount in the first coupon. Then find the FV of an annuity with 8 as the number of periods with the accumulation of discount in the first coupon as the payment and and you will get 33.98.

Given di19 = C(i − g)$v^{20-19+1}$ = C(i − g)$v^{2}$ = 8, So

= C(i − g)$v^{2}$($v^{18}$+$v^{17}$+...+$v^{11}$)

=8$(\frac{1}{1.045})^{10}$ $\frac{1-(\frac{1}{1.045} )^{8} }{0.045}$

=33.98