Final answer:
To calculate the bond's price when its interest rate is less than the market interest rate, you need to calculate the present value of the bond's future cash flows. Using the formula P = CF / (1 + r) + CF / (1 + r)^2 + ... + CF / (1 + r)^n, where P is the bond's price, CF is the cash flow, r is the discount rate, and n is the number of periods, we find that the bond's price is approximately $1,086.99 when the interest rate is 12%.
Step-by-step explanation:
To calculate the bond's price when its interest rate is less than the market interest rate, we need to calculate the present value of the bond's future cash flows. The expected payments from the bond one year from now are $1,080, which accounts for the final interest payment and the repayment of the original $1,000. Given that interest rates are now 12%, we can use the formula P = CF / (1 + r) + CF / (1 + r)^2 + ... + CF / (1 + r)^n, where P is the bond's price, CF is the cash flow, r is the discount rate, and n is the number of periods. Assuming an annual coupon payment of $70 for 6 years, we have:
- P = $70 / (1 + 0.12) + $70 / (1 + 0.12)^2 + ... + $70 / (1 + 0.12)^6 + $1,000 / (1 + 0.12)^6
- P = $62.50 + $55.80 + ... + $26.57 + $562.28
- P = $1,086.99
Therefore, the bond's price is approximately $1,086.99 when the interest rate is 12%.