Final answer:
To determine the year 6 accumulation of discount for the 20-year bond, we calculate the present value of coupon payments and face value at year 6, using a 10% discount rate for the first ten years and a 6% thereafter, then subtract the price paid for the bond using the 10% yield up to year 6.
Step-by-step explanation:
To determine the amount for accumulation of discount for year 6 of the bond, we need to calculate the present value of the bond's cash flows using the present value formula at different discount rates for different periods. During the first ten years, the bond is purchased to yield 10%, and it yields 6% thereafter. The bond pays 2% annual coupons, which corresponds to $20 each year, since the face value of the bond is $1,000.
For the first ten years, the discount rate is 10%. For the last 10 years, from year 11 to year 20, the discount rate is 6%. To find the accumulation of discount for year 6, we calculate the present value of coupon payments and face value at year 6, basically treating it like a bond with 14 years to maturity (with a different yield after 10 years), then subtracting the price paid for the bond using the 10% yield to maturity up to that point.
Calculations can be done as follows:
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Let's walk through the calculations based on the example of a simple two-year bond detailed in the question. If the bond is worth $3,000 and pays an 8% coupon, the cash flows would be $240 at the end of the first year and $3,240 at the end of the second year. The present value at an 8% discount rate would be calculated as:
PV = $240 / (1 + 0.08) + $3,240 / (1 + 0.08)^2
If interest rates rise and the discount rate is now 11%, the present value at this new rate would be:
PV = $240 / (1 + 0.11) + $3,240 / (1 + 0.11)^2
Applying a similar approach, but for different periods and rates, and then subtracting the bond's price determined by the 10% yield up to year 6, gives us the accumulation of discount.