a $1,000 bond with a coupon rate of 4% has quarterly coupons and is redeemable after an unspecified number of years at $951. the bond is bought to yield 11% convertible semiannually. if the present value of the redemption amount is $353.20, find the purchase price using the makeham formula. then check your answer using another price formula. (round your answer to the nearest cent.)

A bond's coupon rate can be calculated by dividing the security's total annual coupon payments by the bond's par value. For example, a bond with a face value of $1,000 that pays a coupon of $25 semi-annually has a coupon rate of 5%.

Evaluating the purchase price :

Purchase Price = (g / j) x (C-K)+ k

F = $1,000

r = 4% / 4 = 1%

C = $951

j = (11%/2+1)^(1/2)-1 = 0.027132

K = $353.20

g = ((Fr)/ C)

= (1000 × 1%)/951

= 0.0105152.

Makeham formula :

The Makeham formula is a mathematical formula that expresses the present value of cash flows in terms of repayments rather than the payments themselves. This formula is largely ignored in the financial literature, but as this paper shows, it has many useful applications in fixed income analysis.

Makeham's formula:

Purchase Price = (g / j )( C - K ) + K

Purchase Price =(0.010515/0.027132) × (951-353.20)+353.20

Purchase Price = $ 376. 3677.

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