Bond Valuation | Exam FM | Financial Mathematics Lesson 21 - JK Math

How to Value the Price of Bonds (Financial Mathematics Lesson 21)

In this lesson we learn about bonds and how to calculate their price given its components of its face value, redemption value, coupon rate, and its yield rate. We discuss what each of these components are and their importance to the calculation of a bond’s price.
Bonds are similar to loans in that they are a way to borrow money. Essentially, a bond is a debt that typically requires periodic payments known as “coupons” for a stated term, as well as a one time payment of the amount borrowed at the end of the term issued. We use this definition of a bond to derive its price formula, which is the present value of the coupon payments plus the redemption value. We look at one example problem and discuss what it means to purchase a bond at either par value, at a discount, or at a premium.

This course is designed to help students understand the concepts of mathematics of investment and credit, as well as provide a starting point in preparation for the Actuarial Exam FM (Financial Mathematics).

Financial Mathematics requires a proficient understanding of Calculus concepts such as derivative and integration techniques. This implies that a solid understanding in various algebra skills, including manipulating equations, basic factoring methods, solving logarithmic equations, and more, are also required to fully comprehend and learn the concepts of the Financial Mathematics course.

Video Chapters:
0:00 What is a Bond?
0:49 Components of a Bond
5:02 Finding the Price Formula
8:51 Example Problem
15:48 Effects of Yield Rate & Coupon rate
18:32 Buying at Par, Discount, and Premium

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[JKMath]

⬇Download my FREE worksheet set for all my Financial Mathematics videos!

[boedickson]

Dear Josh, thank you for your painstaking efforts in making these tutorials. Really appreciate the content.

[dd-kjtb]

Hey @JKMath, it's a small request, I'd really appreciate if you could do some videos for Sinking Funds too. Your videos are really comprehensive and easily understandable :)

[hilmehakqimmohdyussof]

thankyou for your video and explanation, i really really like it and appreciate it so muchhh ❤

[BalnurYeraly]

You are such a kind person🥰🥰. Thank you so much for making these videos. Truly Appreciate it🙏

[sandrukshan]

Tgnk you for theese videos are really helpful❤😊

[zeegy]

For the coupons, does the NPV account for the FV of all of the coupons being paid at different times? To me it seems like you only discounted the $1000 lump sum at the end appropriately

[EjBei]

This video was very helpful, but I am still kind of confused about premiums and discounts. Correct me if I am wrong on any of these. What perspective should I view this as? The bond issuer or the bond investor? Would the discount and premium be beneficial or unbeneficial for either party? and what does the yield rate actually do in terms of this? Does the yield rate calculate the interest being paid per coupon? And would the "r" rate just to calculate the "base" value of a coupon per period?

[bryanliu]

I have always had trouble understanding the "price" of a bond. The price is the present value of how much the borrower is paying back to the lender, hence the formula seems to make a lot of sense. However, if an investor buys a bond (i.e. they are the lender), then the amount the investor invests is the face value of the bond, is it not? Because that is how much they are paying (loaning) at time zero. But for some reason, in the fm exam practice questions, the amount invested in the bond is equal to the price of the bond, which I find confusing. Please clarify?

[pochenlai]

Hi! I was doing FM Sample question and one question leads me circle back to reviewing this(problem 65 that starts with “John made a deposit of 1000 into a fund…”.
It’s an annuity due problem which the final solving equation happens to look like the bond price formula but substitute the an with än, so it comes to my mind that what if the coupon of the bond is paid at the beginning of the year, for example a n-year bond, the formula will be 『P= F*R*än + C*v^(n-1)』 or equivalent to『 P= F*R*an-1 + C*v^(n-1)+F*R 』(viewing from having normal coupon bond plus another coupon when bond is purchased)
am I on the right track?( just want to make sure that the redemption values will have to discount to (n-1) but not simply n )

[muhamadizwanbinnasri]

how about if the question gives interest rate (i) and sinking fund earning (j)