The Wild Rose Company has $1000 par value bonds outstanding at 9% interest

Price of the bond can be calculated by the following formula:

Bond price = Present value of interest payment + Present value of bond payment at maturity

Annual bond interest = 9% * $1000 = $90

Bond interest payments will be annual every year, so it is an annuity. Bond payment at maturity is a one time payment. The interest rate that will be used in calculating the required present values will be the yield to maturity rate, which is 7%, with 15 periods.

Now,

First we will calculate the present value of interest payments:

For calculating the present value, we will use the following formula:

PVA = P * (1 - (1 + r)^-n / r)

where, PVA = Present value of annuity, P is the periodical amount = $90, r is the rate of interest = 7% and n is the time period = 15

Now, putting these values in the above formula, we get,

PVA = $90 * (1 - (1 + 7%)^-15 / 7%)

PVA = $90 * (1 - ( 1+ 0.07)^-15 / 0.07)

PVA = $90 * (1 - ( 1.07)^-15 / 0.07)

PVA = $90 * ((1 - 0.36244601964) / 0.07)

PVA = $90 * (0.63755398035 / 0.07)

PVA = $90 * 9.10791400511

PVA = $819.71

Next, we will calculate the present value of bond payment at maturity:

For calculating present value, we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value = $1000, PV = Present value, r = rate of interest = 7%, n= time period = 15

now, putting theses values in the above equation, we get,

$1000 = PV * (1 + 7%)¹⁵

$1000 = PV * (1 + 0.07)¹⁵

$1000 = PV * (1.07)¹⁵

$1000 = PV * 2.75903154072

PV = $1000 / 2.75903154072

PV = $362.45

Now,

Bond price = Present value of interest payment + Present value of bond payment at maturity

Bond price = $819.71 + $362.45 = $1182.16