Question

How much would you pay for a Canada Savings Bond with a face value of $1,000 that offers a 6% coupon (paid in two semi-annual payments starting in six months) and matures in 13 years? Prevailing interest rates are 5% compounded semi-annually. The bond is worth $ . (Round the final answer to the nearest cent as needed. Keep all decimal places as you work through the problem.)

Answer 1

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

Semi annual bond interest = 6% * $1000 * 1/2 = $30

Bond interest payments will be semi 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 semi annual market rate, which is 5% /2 = 2.50%, with 13*2 = 26 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 = $30, r is the rate of interest = 2.50% and n is the time period = 26

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

PVA = $30 * (1 - (1 + 2.50%)^-26 / 2.50%)

PVA = $30 * (1 - ( 1+ 0.0250)^-26 / 0.0250)

PVA = $30 * (1 - ( 1.0250)^-26 / 0.250)

PVA = $30 * ((1 - 0.52623472141) / 0.0250)

PVA = $30 * (0.47376527859 / 0.0250)

PVA = $30 * 18.9506111436

PVA = $568.5183343

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 = 2.50%, n= time period = 26

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

$1000 = PV * (1 + 2.50%)²⁶

$1000 = PV * (1 + 0.0250)²⁶

$1000 = PV * (1.0250)²⁶

$1000 = PV * 1.90029270078

PV = $1000 / 1.90029270078

PV = $526.2347214

Now,

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

Bond price = $568.5183343 + $526.2347214 = $1094.75

So, the bond is worth $1094.75