You will be able to explain how a T-bill pays interest without a coupon and work out what you receive.
Arjun applies for S$10,000 of six-month T-bills through his bank app. Two days later he checks his account and sees S$10,000 has gone out, then a few days after that a smaller sum comes back. Six months on, S$10,000 lands in his account. At no point does anything called interest appear on his statement. He wonders whether he earned anything at all. He did. He was paid up front, in the price.
A Treasury bill, or T-bill, is a short-term loan to the Singapore Government. Like the bonds in module 1, it has a face value and a maturity date. Unlike them, it has no coupon. Nothing is paid to you while you hold it.
Instead, you buy the bill for less than its face value and receive the full face value when it matures. The gap between what you pay and what you get back is your interest. If you pay S$9,800 for a bill with a face value of S$10,000, the S$200 difference is everything you earn.
In the table you built in lesson 1.4, Read a bond's terms and fill in its cash flow table, a T-bill has just two rows: money out on the issue date and face value back at maturity.
Singapore T-bills run for a year or less. MAS issues them on a published schedule, and the tenors on offer, such as six months and one year, are listed on its website. Check the current list there rather than relying on what a friend bought.
Arjun's bank, like many, took the full face value from his account when he applied and refunded the discount after the auction. That is why he saw S$10,000 leave and a smaller sum come back. Your bank's T-bill page will say how it handles the payment.
A S$200 gain is hard to compare with anything until you know how long it took and how much you put in. So the discount is quoted as a yearly yield, the same way a fixed deposit rate is quoted per year whatever its term.
The method has two steps. First, divide the gain by what you paid, not by face value. Then scale it to a year by multiplying by 365 and dividing by the number of days the bill runs.
Take a made-up example: S$9,800 paid for a S$10,000 six-month bill that runs 182 days. The gain is S$200, and S$200 divided by S$9,800 is about 2.04% for the six months. Multiply by 365 and divide by 182, and you get about 4.09% a year, which rounds to about 4.1%.
Two common slips are worth avoiding. One is dividing S$200 by S$10,000, the face value, which gives 2% for six months and understates the yield, because your money in was S$9,800, not S$10,000. The other is forgetting the bill only ran half a year and calling the 2.04% the yearly rate.
In practice you usually start from the other end. The auction, which lesson 4.2 explains, produces a cut-off yield, and you want to know what you will pay and earn.
Run the method backwards. Price equals face value divided by one plus the yield times the days over 365.
With a made-up cut-off yield of 3.2% on a 182-day bill with a face value of S$10,000, that is 10,000 divided by 1 plus 0.032 times 182 over 365. The bracket comes to about 1.01596, so the price is about S$9,842.94, and the interest you earn is about S$157.06.
Here a different slip creeps in. Half of 3.2% on S$10,000 is S$160, which is close but not right, because the yield is earned on the lower price you pay, not on face value. The gap is small on one bill, but getting the method right now saves confusion when you compare bills, deposits and SSBs later.
For a one-year bill, the days are close to a full year, so the price is roughly face value divided by one plus the yield.
The quoted T-bill yield is a simple yearly rate for the life of the bill. It does not compound within the six months. If you roll one six-month bill into another at the same yield, you earn interest on your interest, and the effective yearly figure ends up slightly higher. At the 4.09% example, rolling twice in a year works out to about 4.12%.
That is the same idea as the gap between a quoted rate and the effective rate in How money works, lesson 3.1, Advertised rate, APR and EIR are three different numbers. For comparing a T-bill with a fixed deposit of the same term, the quoted figures are close enough to line up directly.
Arjun's statement made sense once he saw it this way. His interest was the refund he had barely noticed. Now try the method on a one-year bill at two different cut-off yields and see how much a single point changes what you pay.
Using made-up figures, work out the amount paid and interest earned on a S$10,000 one-year T-bill at cut-off yields of 3% and 4%.
Junxiong-WFG Organisation is an authorised representative of AIA Financial Advisers Private Limited (Reg. No. 201715016G).