Problem #3: There is a bond on a company\'s books with an original term of 10 ye

Question

Problem #3: There is a bond on a company's books with an original term of 10 years that was purchased for a premium at its issuance, just over 2 years ago. The bond pays semi-annual interest. With the receipt of the latest coupon, the corresponding amount for amortization of the premium was S137.33. Exactly one year ago, the amount for amortization of the premium was S125.52. Based on the relation between subsequent amounts for amortization of the principal, what was the original value of the premium? Problem #3: Answer correct to 2 decimals Just Save | | Submit Problem #3 for Grading

Explanation / Answer

Solution:

Amortization in 4th semiannual period = $137.33

Amortization in 2nd semiannual period = $125.52

Effective semannual rate of interest = $125.52 (1+i)^2 = $137.33

(1+i)^2 = 4.60%

Therefore amortization of Premium at 1st semiannual period = $125.52 / 1.046 = $120

Now premium amoritzation will increase by 4.60% every semiannual period for 20 semi annual periods

Therefore original value of permium will be total amortization for 20 semiannual period

Hence original value of premimum = $3,804.24

Computation of Premium Amortization Semiannual Period Premium Amortization 1 $120.00 2 $125.52 3 $131.29 4 $137.33 5 $143.65 6 $150.26 7 $157.17 8 $164.40 9 $171.96 10 $179.87 11 $188.15 12 $196.80 13 $205.86 14 $215.32 15 $225.23 16 $235.59 17 $246.43 18 $257.76 19 $269.62 20 $282.02 Total $3,804.24

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