Finding the Purchase Price and Discount

Question

Find the purchase price and discount of a 12% 15000 bond maturing in 10 years to yield the buyer 15% compunded monthly and redeemable at par

Answer 1

Hi Earl,

The answer can be found using a financial calculator. Please see below for explanation:

A) Purchase price: Since the bond is issued at discount (Stated interest rate is less than market interest rate), the bond value will decline, in other words its purchase price will be less than the par value of $15,000. Input the following in your calculator to find the purchase price, keep in mind you have to solve for PV (Present Value):

1) FV (Future Value): This is the amount the bond will be redeemed at, in this case its $15,000.

2) PMT (Monthly payments) = $150 (12%/12 months * 15,000)

3) I/Y (Market interest rate) = 1.25% (15%/12 months)

4) N (Number of periods) 120 (10 years * 12 months)

-Note: We divided inputs #2 & #3 by 12 because the bond compounds on a monthly basis, and the interest rates are given on an annual basis.

Once you input the above information into your calculator, you will get $12,675.64, which is the bond purchase price.

B) Discount Amount: To find the discount amount, you subtract the par value from the purchase price. That being said, the discount amount = $15,000 - $12,675.64 = $2,324.36

Please let me know if you have any questions.

Thank you,

Ahed