Question

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 $563.27. Exactly one year ago, the amount for amortization of the premium was $534.04. Based on the relation between subsequent amounts for amortization of the principal, what was the original value of the premium?

Answer 1

Not to throw any shade, but answer #1 is very wrong.

Below should be the solution:

From the question, we know that:

n = (10)(2) = 20

4 coupon payments have already happened, with the 2nd payment containing a premium amortization of 534.04, and the 4th containing a premium amortization of 563.27.

Using the formula for amortization of loan repayment: K is the coupon payment every half a year.

Principal repaid at time t = (K)((1/1+i)^(n-t+1))

The coupon payment is also represented by Fr, with F being the face value, and r being the coupon rate.

Therefore Principal repaid at time t = (Fr)((1/1+i)^(n-t+1))

From the relation of the 2 premium amortizations, we know that:

563.27 = 534.04 ((1+i)^2)

From the above equation, we get that i is approximately 0.027.

Therefore, each coupon payment is 534.04(1.027^(20-2+1)) = 885.99.

Then using the prospective method for loan repayment (the premium is essentially the outstanding balance at time 0), we have:

Premium = 885.99(annuity present value factor: n = 20, i = 0.027)

             =  13554.22

Answer 2

Amount amortised in one year period = $563.27 - $534.04 = $29.23

Amortisation per period = Original Amount of Premium / Term of the bond

$29.23 = Original Amount of Premium / 10

Original Amount of Premium = $29.23 * 10 = $292.3

Original value of premium = $293.3