Do you mean the market price or the redemption value?
The bonds yield stays in line with market rates (if low risk). So if rates rise yield must rise which means price comes down and vice versa.
If the bond price is at par (£100%) then the coupon=yield=market interest rate.
With a junk bond, say coupon 10%, the bond price will be lower than the face value due to the risk of default. So answer is no.
Mirroring and adding to below answers:
"Will the bond proceeds always be greater than the face amount of the bonds when the contract rate is greater than the market effective rate of interest ?"
Yes, the bond is sold at a premium since a new issue on the market with similar maturity and risk will have a lower coupon rate.
"why is the investor will to invest in this type of bonds?"
The promised interest payments for the life of the bond is higher than the market, and insititutions can amortize the premiums in order to reduce their tax liability, so they can benefit from the higher income and lower taxes that result from premium amortization.
Will the bond proceeds always be greater than the face amount of the bonds when the contract rate is greater than the market effective rate of interest
Yes
When the market rate is less than the contract rate the bonds are sold at a premium; more than the face value.
and why is the investor will to invest in this type of bonds?
Investors looking for guaranteed cash flows will invest in these types of bonds because the guaranteed interest revenue will be higher than they could get with other types of investments.
Will the bond proceeds always be greater than the face amount of the bonds when the contract rate is greater than the market effective rate of interest and why is the investor will to invest in this type of bonds?