Principal: The Amount Borrowed and Owed Back
Principal is the amount a bond issuer has agreed to repay. The principal is the base the contracted coupon rate is struck on, and it is the sum that comes back at the end. Principal is not the amount paid for the bond, and on a bond that repays in instalments the amount owed falls over the life while the interest falls with it.
Nothing named below exists anywhere
The ten year 8.50 per cent bond, the zero coupon bond, the amortising variant, Palash Cements Limited and the five year government spot rate were assembled for this guide so that arithmetic could be worked in the open. The ten year 8.50 per cent bond has no issuer. Rating scales belong to the firms that publish them, so Palash Cements Limited carries no rating.
The amortising variant is a special case worth flagging before its numbers arrive. The record supplies its shape and not one figure for it. Every rupee in its schedule below was therefore constructed from the same face amount and the same contracted coupon rate as the bond that repays at the end, and then computed row by row.
Why does a promise need a quantity as well as a calendar?
A bond fixes what is owed and when. The promise has two halves doing quite different jobs. The calendar half is a list of dates. The other half is a single number sitting behind all of them, and every dated obligation is expressed against it. Without the number, the dates have nothing to carry.
The principal is that number, and it is the quantity every other term of the bond attaches itself to. The interest is a rate on it. The repayment is a return of it. The document that carries the promise defines it once, near the top, precisely so that everything below has something fixed to point at. Nobody could compute what was owed on any of its dates, so a contract that named dates and a rate but never named an amount would not be an incomplete contract but no contract at all.
Here is the domestic version, and it is worth a moment because the structure is identical. A vegetable seller borrows Rs 30,000/- from a lender who charges 2 per cent a month. The two of them have agreed on a rate and on a set of dates, and neither of those settles anything on its own. The Rs 30,000/- is what settles it. Two per cent of Rs 30,000/- is Rs 600/- a month, and if the seller had borrowed Rs 45,000/- at exactly the same rate on exactly the same dates the monthly payment would be Rs 900/-. Nothing about the rate changed. The base did, and the base is what the rate had to be pointed at before it produced a rupee amount at all.
The base and the rate together are the whole of the subject in one paragraph, and every harder case is the same idea with more places to go wrong. The rate is printed in large type on the front of every document, and the rate is never where readers go wrong. The base is where they go wrong. The base is assumed rather than read, and three plausible candidates sit nearby waiting to be substituted for it.
What is the principal of a bond?
The principal is the amount the issuer has agreed to repay. The definition is that short and it is complete. A category is what stops the principal being confused with its neighbours, so naming what kind of thing a principal is does more work than any addition to the definition.
Principal is a term of the obligation, not a measurement of anything. The claim is about categories rather than about bonds. A measurement is something taken, and it can come out differently on Tuesday because the thing being measured moved. A contract term is something that was written down, and it comes out the same on Tuesday because nobody has opened the document. The principal belongs to the second kind. Four things leave the principal exactly where it was: the bond changing hands, somebody paying more or less for it than the last person did, rates going anywhere, and the issuer having a spectacular year.
Try the household form of it. Somebody borrows Rs 1,000/- from a neighbour and the neighbour writes the amount on a slip of paper. The neighbour then has an urgent need for cash. The third person wants a bit of profit for waiting, so the slip changes hands for Rs 850/-. The borrower now owes Rs 1,000/-. Not Rs 850/-. Nothing that happened between the neighbour and the third person was a conversation the borrower was part of, and no amount of trading among strangers can quietly rewrite what somebody signed for. The amount owed is fixed in the document. The price the document changes hands for is a separate story with separate participants.
The slip of paper does a great deal of work. The example has already separated three quantities that a first-time reader treats as one, and it did so without any finance in it at all. The three quantities will try to merge back together, helped by the fact that in the first case anybody meets, all three are the same number.
Which three amounts get merged into one?
Three amounts sit around every bond and every one of them is expressed in rupees. The shared unit is most of the reason they collapse into each other in a reader's head. Take them one at a time and give each its own sentence.
The first is what the issuer received when the bond was issued. Money came in through the door on the day the instrument was sold, and that amount is a fact about a day in the past. The second is the principal, the amount the issuer owes. The amount owed is a fact about the document and it holds for the whole life. The third is what a later buyer hands over to take the claim off somebody else. The purchase price is a fact about one transaction between two people who are not the issuer, and there can be dozens of such facts across a life, all different.
All three can be the same number, and usually they are not. The confusion is not careless reading, and it deserves more sympathy than it normally gets. The three amounts are the same number in exactly the one case a reader meets first: a bond issued at its face amount and bought by its first holder. In that case the issuer received Rs 1,000/-, the issuer owes Rs 1,000/-, and the holder handed over Rs 1,000/-. Three quantities, one figure, and no reason on the face of it to suspect they are three.
Then the first holder sells to somebody else a year later at Rs 879.70/-, and the third quantity comes loose from the other two while the reader is still carrying a mental model in which there was only ever one. The first resale is the moment the model breaks, and it breaks quietly rather than with an error message.
An issuer raised Rs 559.47/- and owes Rs 1,000/-. Which of those two is the principal?
What is the contracted coupon rate actually struck on?
One sentence carries most of the subject, and it is worth stating flatly before it is explained. The contracted coupon rate is applied to the principal. The rate is not applied to the price somebody paid. The rate is not applied to the value of the claim today. The rate is not applied to the issuer's earnings this year. None of those three quantities is written into the sentence that produces the payment, so none of them can move the rate.
Write the base beside the rate, in the same breath, every single time. Not as a stylistic nicety and not as a habit for careful people. A rate is a pure ratio and a ratio is not an amount until something has been divided by something. Until what the 8.50 per cent is 8.50 per cent of has been said, only half an instruction is in hand, and the missing half is the half a reader supplies from whatever number happens to be nearest.
| It | the interest falling due at the end of year t, in rupees |
| c | the contracted coupon rate, as a decimal, written into the document and never moving |
| Pt | the principal outstanding during year t, in rupees, which is the base |
Put the invented instrument through it while the notation is still in view. Principal on the ten year 8.50 per cent bond is Rs 1,000/-, and it stays outstanding at Rs 1,000/- from the first day to the last, with one payment date a year. So year one applies 8.50 per cent to a base of Rs 1,000/- and produces Rs 85.00/-. Year two applies the same rate to the same base and produces Rs 85.00/- again. The interest comes out at Rs 85.00/- ten times, and the reason it repeats is not that the rate is fixed but that the base is.
Hold on to that last distinction. Everything that follows turns on it. The interest repeated because two things stayed still, and the rate was only one of them. A reader who has only ever met bonds that repay at the end has never had those two things move independently, so they have had no occasion to notice that there were two of them.
The everyday parallel is a shop on rent. A tenant agreed to pay Rs 25,000/- a month, and later somebody buys the shop from the landlord for a figure the tenant never sees and would not care about. The rent is Rs 25,000/- a month. The rental agreement fixed it, and the rental agreement is a different document from the sale deed, signed by different people on a different day. The idea that a purchase price could reach across and reset a rent is obviously wrong the moment it is said out loud about a shop. Both figures are printed in the same rupees on the same screen, so the same idea is exactly as wrong about a bond and much less obvious there.
The ten year 8.50 per cent bond is bought at Rs 879.70/-. What interest will the issuer pay each year?
Does the amount owed stay put for the whole life?
Not necessarily, and this is where the subject stops being a matter of definition and starts being a matter of arithmetic. Consider the ten year 8.50 per cent bond first. Its outstanding amount reads Rs 1,000/- on the first day, reads Rs 1,000/- on the last, and then all of it is repaid on one date. The flat shape has a name: it is a bulletA repayment shape in which the whole amount owed lands on a single date at the end, with nothing paid down along the way. The repayment event on that date is covered separately., and it is the shape that lets a reader believe the principal is simply a constant.
Now take the other shape. A bond can hand the principal back in pieces spread across the life instead of parking all of it at the end. The amortising variant built here does exactly that: ten equal instalments of Rs 100.00/- on the same ten annual dates as the interest. After the first instalment the issuer owes Rs 900.00/-. After the second, Rs 800.00/-. After the tenth, nothing, and the obligation is finished. The amount outstanding is not one number across the life; it is ten numbers, one for each year.
If the interest is a rate on what is outstanding, then the interest must fall as the outstanding amount falls, without the rate changing at all. Falling interest follows with no extra assumption from the sentence above. Falling interest is not a new rule about amortising bonds. The old rule about bases has simply met a base that finally moves.
Work the interest against that staircase and the consequence arrives in rupees. Year one applies 8.50 per cent to a base of Rs 1,000/- and gets Rs 85.00/-. Year two applies it to Rs 900.00/- and gets Rs 76.50/-. Follow that down the years and the tenth applies the very same 8.50 per cent to Rs 100.00/- and gets Rs 8.50/-. The final year's interest is one tenth of the first year's, and the rate that produced both was the same 8.50 per cent.
| Pt | the principal outstanding during year t, in rupees |
| F | the face amount, here Rs 1,000/-, which is what is outstanding on day one |
| n | the number of equal instalments, here ten, one on each annual date |
| t | which year it is, running from one to ten |
A table of ten rows is where the reader can check the claim instead of accepting it, so set the whole schedule out rather than describing it. Every figure below was computed from the Rs 1,000/- face amount and the 8.50 per cent contracted coupon rate, and nothing in it was carried across from anywhere.
| Year | Principal outstanding | Interest at 8.50 per cent | Principal repaid | Total that year |
|---|---|---|---|---|
| 1 | Rs 1,000.00/- | Rs 85.00/- | Rs 100.00/- | Rs 185.00/- |
| 2 | Rs 900.00/- | Rs 76.50/- | Rs 100.00/- | Rs 176.50/- |
| 3 | Rs 800.00/- | Rs 68.00/- | Rs 100.00/- | Rs 168.00/- |
| 4 | Rs 700.00/- | Rs 59.50/- | Rs 100.00/- | Rs 159.50/- |
| 5 | Rs 600.00/- | Rs 51.00/- | Rs 100.00/- | Rs 151.00/- |
| 6 | Rs 500.00/- | Rs 42.50/- | Rs 100.00/- | Rs 142.50/- |
| 7 | Rs 400.00/- | Rs 34.00/- | Rs 100.00/- | Rs 134.00/- |
| 8 | Rs 300.00/- | Rs 25.50/- | Rs 100.00/- | Rs 125.50/- |
| 9 | Rs 200.00/- | Rs 17.00/- | Rs 100.00/- | Rs 117.00/- |
| 10 | Rs 100.00/- | Rs 8.50/- | Rs 100.00/- | Rs 108.50/- |
| Across the life | Rs 5,500.00/- | Rs 467.50/- | Rs 1,000.00/- | Rs 1,467.50/- |
The bottom row of the second column looks odd at first sight and it is the most useful cell in the table. Rs 5,500.00/- is not an amount anybody ever owes. Rs 5,500.00/- is the ten outstanding balances added together, and that sum is the quantity the 8.50 per cent was really applied to across the whole life, one year at a time. Multiplied out, the sum gives Rs 467.50/- exactly, and the interest column summed independently gives the same figure. On the bullet, the ten outstanding balances add to Rs 10,000.00/-, whose 8.50 per cent is Rs 850.00/-.
| I | the interest across the whole life, in rupees |
| c | the contracted coupon rate, as a decimal, the same on both shapes here |
| Pt | the principal outstanding during year t, in rupees |
| n | the number of years the obligation runs, here ten on both shapes |
Only the bases are left once the rate cancels out of the comparison, and a single line then explains the whole difference between the two shapes without any appeal to how bonds work. Two instruments, one contracted coupon rate, and the interest differs by Rs 382.50/-. Every rupee of that difference is the difference between Rs 10,000.00/- and Rs 5,500.00/- of outstanding balance, multiplied by 8.50 per cent. Nothing else moved and nothing else could have.
Two bonds are each written for Rs 1,000/- and both carry a contracted coupon rate of 8.50 per cent. One repays at the end, one in ten instalments. Which promises more interest, and why?
On the amortising variant the contracted coupon rate reads 8.50 per cent in every year, and the interest falls from Rs 85.00/- to Rs 8.50/-. What fell?
What does a zero coupon bond owe, and what did it raise?
Before the arithmetic, a question worth sitting with. Can a bond promise no interest at all and still be a bond? The answer is yes, and the instrument that does it turns out to be the clearest picture of principal available anywhere in this guide.
A zero coupon bond promises a single payment on a single date and nothing before it. There is no interest date, no coupon amount, and no schedule to speak of. An amount owed and a date it is owed on are all there is, and that is enough to be an obligation. The return to a buyer comes from handing over less than the amount owed and waiting.
Because nothing is paid along the way, the amount raised and the amount owed are visibly different numbers sitting next to each other, and no reader can merge them. The distinction is the same one drawn in small print above, redrawn so large that missing it is not an option. A zero coupon bond teaches principal precisely because it has no coupon to teach.
Here are the two numbers. The zero coupon bond promises Rs 1,000/- at one date, and that date falls 7.119062643353 years out. Discount that single payment at 8.50 per cent a year, one step a year, and the bond prices at Rs 559.47/-. A buyer at that price hands over Rs 559.47/- and is owed Rs 1,000/-, and the gap between them is Rs 440.53/-. Nobody looking at Rs 559.47/- beside Rs 1,000/- is going to mistake one for the other.
Two things about that price need saying rather than assuming, and both of them are about being able to reproduce a figure rather than about bonds.
The first is the compounding convention, and it belongs beside the rate rather than in a footnote. A rate in this guide is quoted for one year, charged once inside that year, and used to discount at the same once-a-year step. The convention is not trimming attached to the number; it is half of what the number means. Squeezing the same quoted figure into more frequent steps within the same twelve months makes the identical promise come out at a different price. A figure printed without its convention cannot be rebuilt by whoever reads it. The convention belongs beside the number the way a unit belongs beside a weight.
The second is a precision point, and it is the sort of thing that makes a careful reader doubt themselves for no reason. The maturity above is carried to twelve decimal places. Rounded to 7.1191 years, the same arithmetic gives Rs 559.46/-, one paisa lower. Neither figure is a mistake; they belong to two different maturities, one rounded and one not. A reader handed the short maturity and the long price would work it through, land a paisa away, and wrongly conclude the error was theirs. So both figures are printed here, with the rounding that produced each one named beside it, and the long maturity is the one the arithmetic in this guide uses.
Before reading on: can a bond promise no interest at all and still be a bond?
How do three instruments built on one rate compare?
Put the three side by side: one instrument teaches a number and three teach the mechanism. All three run on annual compounding, and two of the three share a contracted coupon rate of 8.50 per cent so that the rate cannot be the quantity doing the explaining.
First, the ten year 8.50 per cent bond. Principal Rs 1,000/-, outstanding at Rs 1,000/- from the first day to the last. Interest of Rs 85.00/- ten times comes to Rs 850.00/-, and the principal comes back whole at the end. Everything promised is Rs 1,850.00/-.
Second, the zero coupon bond. The zero coupon bond owes Rs 1,000/- on one date 7.119062643353 years out and owes nothing before it. Everything promised is Rs 1,000/-, all of it principal and none of it interest, and the buyer's compensation for waiting is built into the Rs 559.47/- they handed over rather than paid out along the way.
Third, the amortising variant, constructed here from the same Rs 1,000/- face amount and the same 8.50 per cent contracted coupon rate, repaying in ten equal instalments of Rs 100.00/-. Interest of Rs 467.50/- across the life, principal of Rs 1,000/- handed back in slices, and everything promised is Rs 1,467.50/-.
The contracted coupon rate is identical on the first and third, and the interest differs by Rs 382.50/-. The base the rate was applied to produced every rupee of that difference. Say it in the direction that is easy to get backwards: the amortising variant does not pay less because it is a worse deal or because somebody negotiated the rate down. The borrower had the money for less of the time, so the amortising variant pays less, and the interest is a rate on what is being held rather than on what was once handed over.
A bond repays its principal in ten equal instalments and its contracted coupon rate never changes. What happens to the interest paid each year?
Move the number of instalments and watch the interest follow the base
One control, and it changes one thing: how many equal instalments the principal is repaid in. The face amount stays at Rs 1,000/-, the contracted coupon rate stays at 8.50 per cent a year, and the life stays at ten annual dates. The instalments fall on the last dates of the life, so at one instalment everything lands at the end and at ten instalments the repayment starts immediately. The control opens at one instalment, and that setting is the ten year 8.50 per cent bond itself.
The dashed outline behind the drawing is that opening setting, left in place as a ghost. Every later adjustment is measured against it rather than against nothing, and the sentence under the drawing names the difference in rupees.
Sweep the control once and watch which number refuses to move. The interest total travels from Rs 850.00/- down to Rs 467.50/-, the staircase flattens or steepens, the bars under it shorten from the right, and the 8.50 per cent printed on the strip is the same 8.50 per cent at every setting. The control exists to show exactly that: the base moved and nobody was watching it.
How does anybody actually use this?
A household comparing two loan offers is running exactly this arithmetic without the vocabulary. One lender quotes a rate on the original amount borrowed for the whole term, and the other quotes the same rate on what is still owed. The rate on the poster is identical and the money is not, and the household that only reads the poster will pick wrongly about half the time. One sentence separates the two offers: what is that per cent a per cent of, this month.
A lender writing the document works the other way round. A lender's own funding has to cover the principal outstanding multiplied by the time it stays outstanding, so the lender decides how much it is willing to have outstanding and for how long. A shape that pays the principal down early frees money to lend again and earns less interest for exactly the same reason. Nobody has to choose between those two facts; they are one fact seen from two sides, and the sum of the outstanding balances is where both of them live.
An analyst reading a borrower's obligations sorts them by the same quantity rather than by the headline rate. Rs 1,000/- outstanding for ten years and Rs 1,000/- amortised over ten years are the same face amount and a very different call on cash, and the second one starts repaying while the business still has the money it borrowed. Everybody who does this for a living is tracking the base and its schedule, and the rate is the part they can read in two seconds and then set aside.
One practical warning for anybody reading a real document rather than a worked example. The names attached to the roles around an issue, the arrangerThe party that puts an issue together and places it with the first holders. The arranger fills a role rather than a term of the promise, so nothing it does changes a rupee of what is owed. and the paying agentThe party that actually moves each payment out of the issuer and into the hands of the current holder on the due date. The paying agent handles the money without ever being the one who owes it. among them, will be printed all over it, and none of them changes a rupee of what is owed. Read past them to the quantity.
The error that gets made, and what it costs
Somebody buys the ten year 8.50 per cent bond at Rs 879.70/- rather than at its face amount. The reasoning that follows is not stupid: I hold an 8.50 per cent bond, it cost me Rs 879.70/-, so my interest is 8.50 per cent of Rs 879.70/-, or about Rs 74.77/-. Then the payment arrives and it is Rs 85.00/-, a full Rs 10.23/- more than expected.
The issuer pays Rs 85.00/- because the contracted coupon rate is struck on the Rs 1,000/- principal and nothing about a later purchase price touches it. The buyer substituted a base. The price was the most recent rupee figure they had handled and the sentence in their head had an empty slot in it, so the substitution happened silently, without anybody deciding to make it.
Rs 10.23/- is small, and the smallness is the trap rather than the consolation. The reader now holds a model in which the interest depends on what they paid, and that model will produce a wrong answer on every bond they meet afterwards. Worse, it will be wrong in the opposite direction the moment they buy something above its face amount. Buy the same bond at Rs 1,143.78/- and the same reasoning predicts Rs 97.22/-. The issuer still pays Rs 85.00/-, so the expectation is now Rs 12.22/- too high. The two halves cancel in the reader's memory and leave an impression of roughly getting it right, so an error that flips sign cannot be corrected by experience.
The mistake is made most often by somebody who has met a bank deposit first, and a bank deposit is a reasonable place to arrive from. On a deposit, the amount handed over and the amount the bank owes genuinely are the same number, so the base and the price coincide for years without ever being distinguished. Meeting a bond is the first time those two come apart, and nothing announces it.
The repair is one line. The rate and its base are read out of the same sentence, and on a bond the base is always the principal. A sentence that does not contain a base has not been read to the end.
Why is one substituted number worth this much attention?
Because the contracted coupon rate is meaningless without its base, and because the base is the thing readers substitute without noticing. The two facts together turn a definition into a discipline. Either one on its own would be a sentence.
The cost sits downstream rather than in the arithmetic itself, so follow what goes wrong there. A reader with the wrong base computes the wrong interest. From the wrong interest they read the wrong income out of a holding, and that income is a figure they will then use for something. Then they compare their figure with what the issuer actually paid, find a difference, and go looking for it in the wrong place: in the dates, in the day count, in whether something was deducted, in whether the payment was late. The discrepancy was created three steps earlier by a substitution that left no trace, so every one of those searches is expensive and none of them can succeed.
The base discipline is therefore worth carrying as a habit rather than as knowledge. The substitution does not feel like a decision, so knowing that the coupon is struck on the principal protects nobody. Substituting a base feels like reading. A mechanical rule applied to sentences rather than to bonds is what protects a reader: where a per cent appears, find the word it is a per cent of, and where that word is missing, stop and go and find it.
Carried beyond bonds, that rule keeps paying. Every rate in this subject area has a base, several of them have bases that look alike, and a handful have bases that change over time exactly as the principal outstanding does. A rate on an original amount and a rate on a current amount are two different instructions wearing the same number, and only one habit stands between a reader and that confusion: naming the base before doing anything with the rate.
A reader cannot reconcile the interest they expected with the interest the issuer paid. What should they check first?
Who sets the rules around how much may be borrowed?
Four questions crowd around the amount an issuer borrows, and each is settled by an authority rather than here. How much an issuer may borrow through a bond issue. The disclosure required about the amount raised and the use the money is put to. How a partly paidA structure where a buyer hands over the purchase amount in stages rather than all at once, so the instrument is not fully paid up on day one. Whether and how it may be offered is set by an authority. or instalment structure may be offered to buyers. And the valuation norms that decide the carrying amountThe figure an instrument is shown at in the books of whoever holds it, which is set by accounting and prudential rules rather than by the bond document itself. an outstanding principal is held at in a regulated holder's books.
All four belong to the Securities and Exchange Board of India (SEBI) at sebi.gov.in for corporate debt and to the Reserve Bank of India at rbi.org.in for government securities and for what a regulated holder must do. All four are revised. A requirement that moves is settled by naming the authority that maintains it. The authority holds the current text and any copy holds only the text of the day it was made.
A requirement copied out looks like the more generous option right up to the morning it silently ceases to be correct, and a reader has no way of telling which morning that was. Tax works the same way: the tax authority is at incometaxindia.gov.in. The list of contents required in an offer documentThe document put in front of prospective buyers when an instrument is offered. An authority prescribes what it must contain, and the authority revises that list at the source. falls into the same category, and so does the redemption amountThe sum that falls due when the obligation ends. On the instruments here it equals the principal still outstanding at that point, and the event itself is covered separately. in any case where a document sets it somewhere other than at the face amount.
Where the rules on the amount borrowed actually live
The compounding convention is the only rule the interest figures above lean on, and it had to be stated for those figures to be rebuildable. Every item below is maintained and revised by the body named against it, and the source itself is what settles the question before anybody acts on it.
- How much an issuer may borrow through a bond issue. SEBI, sebi.gov.in, for corporate debt; the Reserve Bank of India, rbi.org.in, for government securities and the money market.
- The disclosure an issuer must make about the amount raised and the use it is put to. SEBI, sebi.gov.in.
- How a partly paid or instalment structure may be offered to buyers. SEBI, sebi.gov.in.
- The valuation norms that decide the carrying amount an outstanding principal is held at in a regulated holder's books. The Reserve Bank of India, rbi.org.in.
- Anything touching the tax treatment of a holding or of the receipts from it. The tax authority, incometaxindia.gov.in.
Why is the amount an issuer is allowed to borrow through a bond issue not stated here?
References
| Source | Named for | Where |
|---|---|---|
| SEBI | How much an issuer may borrow through a bond issue in corporate debt, what must be disclosed about the amount raised and the use it is put to, and how a partly paid or instalment structure may be offered to buyers | sebi.gov.in |
| The Reserve Bank of India | How much may be borrowed in government securities and the money market, and the valuation norms that decide the carrying amount an outstanding principal is held at in a regulated holder's books | rbi.org.in |
| The tax authority | Anything touching the tax treatment of a holding or of the receipts from it, none of which is described above | incometaxindia.gov.in |
Palash Cements Limited, the ten year 8.50 per cent bond, the zero coupon bond, the amortising variant and the five year government spot rate are invented.
Educational material. Not advice on any investment, tax, budget or market position.