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 $$412\mathrm{.}00.$ Exactly one year ago, the amount for

amortization of the premium was $$376\mathrm{.}56.$ 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.