# The tutor shows an example of how to price a bond.

**Example:**

Imagine the following scenario: a 20-yr $10K bond pays at 4% per year, compounded and paid semi-annually. However, realizing a present interest rate of only about 2.5%, a second buyer is happy to buy the bond for 3% yield. How much should the second buyer pay if they buy right after the interest payment at 5 years?

Solution:

Assuming the interest payment at exactly 5 years goes to the previous owner, the second buyer’s first interest payment will be at 5½ years (5 years, 6 months).

To find the purchase price, we find the present value of all the bond’s future interest payments, then its redeem value of $10K.

##### Interest payments:

At half-year intervals, the first being at 5½ years, the last at 20 years, there will be 30 payments total. One way of seeing it: the original purchaser’s first interest received was 6 months after purchase, their last at 5 years in. Therefore, they got 10 payments. The bond pays, in total, 40 payments: 2 per year for 20 years. Therefore, the second buyer gets the other 30 payments.

Each interest payment is $200: the interest is 4% annually, but paid and compounded semi-annually. Therefore, the interest per period is 4%/2 or 2%. 2%x10K=$200.

The second buyer expects only 3% annually, paid and compounded semi-annually. %i is 3/2=1.5.

Here are the inputs:

First, 2nd FRQ 2nd N to clear the financial registers.

0 FV

200 PMT

1.5 %i

30 N

CPT PV

Hopefully you get the answer 4803.1676

##### $10K redeem value:

Next, we find the present value of the $10K redeem value, payable 15 years from today:

10000 FV

0 PMT

1.5 %i

30 N

CPT PV

Hopefully you get the answer 6397.6243.

If the second buyer wants a 3% yield for this bond, they should pay 4803.1676 + 6397.6243 = 11200.79.

HTH:)

Source:

Killip, T. Brian. __Mathematics for Business: the CGA Reference Handbook__. Toronto: Harcourt Brace & Company, 1993.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

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