You will be able to explain with a worked example why a bond's price falls when market yields rise.
Hui Min bought a bond with a 3% coupon at 100. A year later it has five years left to run, and her brokerage app shows it at 95.55. Nothing has gone wrong with the issuer, every coupon has arrived on time, and yet the screen says she has lost almost S$45 on every S$1,000. Her first thought is that someone made a mistake. Nobody did. Interest rates went up, and this lesson shows you exactly why that pushed her price down.
Start with what cannot change. The coupon is fixed in the bond's terms, so Hui Min's bond pays S$30 a year on S$1,000 of face value whatever happens to rates. Lesson 1.1, A bond is a loan with a fixed timetable, called that the bond's promise.
Now suppose new bonds from similar borrowers start paying 4% instead of 3%. A buyer can get S$40 a year on S$1,000 from a new bond. Why would they pay S$1,000 for Hui Min's bond that pays only S$30?
They would not. The only way her bond can compete is on price. It has to sell for less than face value, low enough that the S$30 coupons plus the gain back to face value at maturity add up to the same 4% yield a buyer could get elsewhere. The coupon cannot move, so the price does the moving.
The same logic runs in reverse. If new bonds pay only 2%, a bond paying 3% is more attractive than anything new, and buyers will pay more than face value for it. That is the whole idea: price and yield move in opposite directions because the cash flows are fixed.
Here is the calculation with made-up figures. The bond has a face value of 100, a 3% coupon paid once a year, and five years to maturity. That means five payments of 3 and a final repayment of 100 at the end of year five.
To find what a buyer wants to pay when the market yield is 4%, you discount each payment back to today at 4%. This is the present value method from How money works, lesson 6.3, Present value: what a future promise is worth today. Each payment is divided by 1.04 raised to the number of years until it arrives.
The year one coupon of 3 is worth 3 divided by 1.04, about 2.885. The year two coupon is worth 3 divided by 1.04 squared, about 2.774. Year three gives about 2.667 and year four about 2.564. The last payment is the coupon and the face value together, 103, divided by 1.04 to the power of five, which is about 84.658.
Add them up: 2.885 plus 2.774 plus 2.667 plus 2.564 plus 84.658 comes to about 95.55. So when the market wants 4%, the bond trades at about 95.55 per 100 of face value. That is the number on Hui Min's screen.
Check it from the other side. A buyer who pays 95.55 gets 3 a year, which is about 3.14% on what they paid, plus a gain of about 4.45 when the bond repays 100 in five years. Spread across the five years, those two together come to 4% a year. The lower price is what turns a 3% bond into a 4% investment for the new buyer.
Now run it the other way. Discount the same five payments at 2%, dividing by 1.02 raised to each year instead. The total comes to about 104.71.
So if market yields fall to 2%, the bond is worth about 104.71 per 100. The holder could sell it for a gain of almost S$47 on every S$1,000. The new buyer pays more than face value, collects 3 a year, and loses about 4.71 at maturity when only 100 comes back, and those together work out at 2% a year.
Lay the three results side by side. At a yield of 2% the price is about 104.71. At 3%, equal to the coupon, it is exactly 100. At 4% it is about 95.55. Higher yield, lower price. Lower yield, higher price. The move is not quite symmetrical, either: a one point fall in yield raised the price by about 4.71, while a one point rise lowered it by about 4.45. Module 2 comes back to that shape when it looks at duration.
Here is the part that should calm Hui Min down. Her bond will still pay S$30 a year and S$1,000 at maturity, exactly as promised, as long as the issuer stays able to pay. The price of 95.55 is what she would get if she sold today. If she does not sell, it is only a number on a screen, and it will drift back towards 100 as maturity gets closer, because at maturity the bond is worth exactly its face value.
So price swings matter most to people who might need to sell before maturity. If the money in a bond is for a dated goal, the risk is that rates rise just before you have to sell. Later modules show you two ways round that: matching the maturity to the date you need the money, which is the idea behind the ladder in module 8, and knowing how sensitive a bond is to rates, which lesson 2.3 covers.
Why rates rise and fall in the first place is a separate subject, taught in How the economy hits your wallet: rates, inflation and cycles. Here you only need the direction and the arithmetic. Take the same five-year, 3% bond and run the method at a few more yields, then look at the shape the prices make when you plot them.
Reprice the course's made-up 5-year, 3% bond at yields of 2%, 3%, 4% and 5% using the worked method, and plot price against yield.
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