Final answer:
The bond's price for Investor G, with a par value of $2,100, coupon rate of 9%, and market yield of 12%, is calculated using the present value of an annuity for the coupon payments and a present value of a lump sum for the par value. After performing the proper financial calculations, the bond's price is found to be $1,476, corresponding to option b.
Step-by-step explanation:
To calculate the bond's price when its interest rate is less than the market interest rate, we will use the bond's fixed coupon payments and par value, discounted at the yield to maturity (market interest rate). In this case, the bond has a par value of $2,100, a coupon rate of 9%, and the market's yield to maturity is 12%. This means Investor G will receive $189 (which is 9% of $2,100) annually for 15 years, plus the par value at maturity. The bond's price can be calculated using the present value formula for an annuity (for the coupon payments) and a present value formula for a lump sum (for the par value).
The present value of the coupon payments (PVC) is calculated by:
- PVC = C * [(1 - (1 + r)^-n) / r]
where C is the annual coupon payment, r is the market interest rate (yield to maturity), and n is the number of years to maturity.
The present value of the par value (PVP) is calculated by:
where F is the par value of the bond.
The bond's price is the sum of the present value of the coupon payments and the present value of the par value:
Bond price = PVC + PVP.
Performing the calculations with the given values will provide us with the correct bond price from the options given in the question. From the calculations, we find that the correct bond price is $1,476, which corresponds with option b.