Your broker just called you to suggest investing in the following (plain vanilla) bond:

Face value: $1,000

Coupon rate: 8%

Coupons are paid semi-annually

Maturity: 15 years

Current price: $846.28

However, the particularity of this bond is that it allows the bondholder to buy some "options" that change the main characteristics of the bond. Thus, you have two available choices:

1) For an additional fee of $50, the bondholder may double the coupons starting from year 9 till maturity.

2) For an additional fee of $85, the bondholder may get quarterly coupons instead of semi-annual coupons. The coupon rate in this case becomes 8% with quarterly compounding.

You have to decide today if you want to buy the bond with any of these options. If you buy the bond with an option attached to it, you'll have to pay the current price of the bond without any option (the plain vanilla bond) + the corresponding fee.

1. Is the bond without any option (the plain vanilla bond) selling at a discount, at par or at a premium?
2. What is the YTM of the bond without any option (the plain vanilla bond)?
3. If you require a 10% yield with semi-annual compounding, should you buy the bond with option 1?
4. If you require a 10% yield with semi-annual compounding, should you buy the bond with option 2?

You read in the financial press that economists expect the general level of interest rates to decrease by 2% in the next three years.

1. Consider you buy the bond without any option and the economists' forecasts are realized. If you want to re-sell this bond in three years, will you sell it at a discount, at par or at a premium?