bond value $1000, 8% coupon interest rate 12 years to maturity date, paid annually, what is value of bond when yield to maturity is 7%

To calculate the value of the bond when the yield to maturity is 7%, we need to calculate the present value of the bond's future cash flows, which are the annual coupon payments and the face value of the bond at maturity.

Here are the steps:

1. Calculate the annual coupon payment: This is the bond value multiplied by the coupon interest rate. So, $1000 * 8$80.

2. Calculate the present value of the annual coupon payments: This is the sum of the present values of each annual coupon payment. We use the formula for the present value of an annuity: PV = Pmt * [(1 - (1 + r)^-n) / r], where Pmt is the annual payment ($80), r is the yield to maturity (7$80 * [(1 - (1 + 0.07)^-12) / 0.07] = $680.58.

3. Calculate the present value of the face value: This is the face value of the bond discounted back to the present using the yield to maturity. We use the formula for the present value of a single sum: PV = FV / (1 + r)^n, where FV is the face value ($1000), r is the yield to maturity (7$1000 / (1 + 0.07)^12 = $513.42.

4. Add the present value of the annual coupon payments to the present value of the face value to get the value of the bond: $680.58 +$513.42 = $1194.

So, the value of the bond when the yield to maturity is 7% is approximately $1194.