Term of a 100 face value bond selling at a premium

Question

A bond of face amount 100 is purchased at a premium of 36 to yield 7%. The amount for amortization of premium in the 5th coupon is 1.00. What is the term of the bond?

I have no clue where to start really. I feel a part of that is the wording. I'm not sure how to interpret "The amount for amortization of premium in the 5th coupon is 1.00.". I'm assuming the first sentence means that the price of the bond is 136 and the yield to maturity is 7%. But yeah any help with explaining what the question is asking or help with the question in general would be greatly appreciated.

Answer 1

There is confusion in the text regarding the 5-th coupon. I will try to retell the problem.

1. The face value of the bond is 100
2. The premium of 36 is the overcharge and makes the price of the bond 136.
3. The yield of the bond is 7% meaning the bond pays 7% of the face value on a yearly basis until is bought back by the issuer. Otherwise said, the bond pays 7 each year until maturity.
4. The bond pays back 1 in the fifth year as to cover completely the initial sale price of the bond, including the premium. Therefore, in the first day after the fifth year, the bond pays not only the 7% but also an extra 1. At this time the bond paid 5x(7%)x100+1=36 which covers the premium.
5. The bond is then sold back to the issuer at face value of 100.

For the issuer the bond is a loan. At buy-back time, the issuer expects to have paid exactly the same amount it charged when the bond was issued. For this reason the maturity of the bond- the term is 5 years.