When interest rates rise, bonds previously issued at lower interest rates will sell for less than face value. To calculate the price of the bond in year 2, we need to discount the future cash flows to their present value. The formula for present value of future cash flows can be used to calculate the price of the bond in year 2.
When interest rates rise, bonds previously issued at lower interest rates will sell for less than face value. In this case, the market interest rate increased from 6% to 7% at the end of 2 years, and then to 8% one year later. This means that the bond issued by ABC Inc at a 6% coupon rate will be worth less than its par value.
To calculate the price of the bond in year 2, we need to discount the future cash flows to their present value. The bond has 13 years remaining until maturity at the end of year 15. The coupon payments are $30 (6% of $1,000) every 6 months. The final principal payment is $1,000.
Using the formula for present value of future cash flows, the price of the bond in year 2 can be calculated as follows:
- Calculate the present value of the coupon payments: PV(coupon payments) = $30/(1+0.07/2) + $30/(1+0.07/2)^2 + ... + $30/(1+0.07/2)^26 = $
- Calculate the present value of the principal payment: PV(principal payment) = $1,000/(1+0.07/2)^26 = $
- Add the present values of the coupon payments and principal payment: Price in year 2 = PV(coupon payments) + PV(principal payment) = $
Therefore, the price of the bond in year 2 can be calculated using the formula for present value of future cash flows.