Interest: How It Is Charged and What You Actually Pay

Interest is the price of using somebody else's money for a period. A rate means nothing until two things are attached to it: the period it covers, and the amount it is charged on. A flat rate is charged on the original amount for the whole tenure; a reducing balance rate is charged on what is still owed. One borrowing can carry both figures truthfully.

Almost every confusion about the cost of borrowing comes from a rate arriving without one of those two attachments. Somebody says the rate is nine, or six, or three and a half, and everybody nods, and nobody asks over what and on what. Both questions sound pedantic and neither is. Over what and on what are the only two questions, and once they are answered a flat rate, a monthly card rate and a yearly loan rate all become the same kind of number and can finally be put beside each other.

One borrowing can be worked out as two different rates that are both completely true, one of them always larger than the other, and the whole of that difference sits in the two attachments a rate arrives without.

What is interest actually the price of?

Think about a vegetable seller who buys her stock at four in the morning and sells it by noon. If she is short one morning and a neighbour lends her Rs 2,000/- until evening, she pays something for that. She did not buy the two thousand rupees. She gives those back. She bought the use of them for one day, and the price she paid is rent on time.

Interest is rent on time. A longer borrowing therefore always costs more, even when nothing else about it changes. Rent on time explains why the tenure sits inside every quoted rate. Rent on time explains why paying early reduces what is owed. And it explains why a borrowing has no single price at all until somebody says how long it runs, in the same way that a room has no rent until somebody says how many months.

The Bhosale household, invented, has this in front of it in two forms at once. There is a two-wheeler loan of Rs 82,000/- taken against a Rs 96,000/- vehicle with Rs 14,000/- paid down, running thirty instalments of Rs 3,150/-. And there is one credit card carrying a balance of Rs 48,594/-. Both are rented money. One rents it on a schedule that ends, and one rents it on a schedule the household writes itself each month. The difference between a schedule that ends and a schedule the household writes itself will matter enormously later, and it starts here, with rent on time.

Interest Rate: what does a number become once a period is attached?

An interest rateA number with a period attached, charged on a stated amount. Without both the period and the amount, it is not yet a rate. is not a number. A rate is a number with a period welded onto it. Rent on time is meaningless until somebody says how much time, so strip the period away and what is left cannot price anything.

Take the figure 3.5 and watch what the period alone does to it. The Bhosale household's card carries a contracted 3.5 per cent a month, and that same 3.5 as a yearly figure would be a completely different animal. On Rs 82,000/- held for one year, 3.5 per cent a year on the original amount is Rs 2,870/-. The same three characters read as 3.5 per cent a month, still on the original amount, is Rs 34,440/-. Charge that 3.5 per cent a month on the balance as it stands, with each month charged on the previous month's total, and the year comes to Rs 41,908/-.

Rs 2,870/- and Rs 41,908/- are the same number quoted three ways, and the only things that separated them were the period and the amount it is charged on. That is a spread of more than fourteen times, produced by nothing that anybody said out loud. So the first thing to do with any quoted rate is to say it back with its period attached, out loud, and see whether the person who quoted it agrees.

What is the second thing a rate needs before it prices anything?

The period is the attachment everybody eventually learns to ask for. The second one hides inside the word on, and it is quieter and does far more damage. A rate is always charged on something, and there are only two candidates: the amount originally borrowed, or the amount still owed today. The original amount and the amount still owed are the same number for exactly one instant, at the very start, and they separate from each other with every instalment paid after that.

Here is the household example, and it is worth walking slowly. Meghna Bhosale's household borrowed Rs 82,000/-. In the very first month it owed Rs 82,000/-. By the fifteenth instalment it owed Rs 43,875/-, a little over half. Just before the last instalment it owed Rs 3,121/-. So the phrase the amount owed does not describe one number across this borrowing. The phrase describes thirty different numbers, and a rate charged on the first of them is being charged on money that came back to the lender long ago.

The same rate charged on the original amount and charged on the amount still outstandingWhat is still owed at a given moment, after every instalment paid so far. The amount outstanding falls across the life of a borrowing. produces two completely different prices, and neither party has said anything untrue. This is the whole of the flat and reducing distinction, and everything below is that one sentence worked out in rupees.

A flat rate: charged on the original amount for the whole tenure

A flat rateA rate charged on the amount originally borrowed for the entire tenure, regardless of how much has already been repaid. takes the amount borrowed, applies the rate to it once for every year of the tenureThe length of a borrowing, from the first instalment to the last. The tenure is the number of periods the rate is applied over., and stops thinking about it. A flat rate never looks at what is still owed. A flat rate is the simplest possible arrangement to quote and to compute, and that is precisely why it survives: a shopkeeper can work it out on the back of a bill, and a borrower can check it in fifteen seconds.

On the Bhosale household's loan the arithmetic runs one way only. Rs 82,000/- borrowed, thirty instalments of Rs 3,150/-, so Rs 94,500/- repaid in total repayableEverything paid across the whole borrowing, principal and charge together. The total repayable is the one figure that cannot be quoted two ways. and a charge of Rs 12,500/-. Thirty months is two and a half years. So Rs 12,500/- divided by Rs 82,000/-, divided again by two and a half, is 6.10 per cent a year, flat. The 6.10 per cent is arithmetically perfect and completely honest, and it is also the smaller of the two true descriptions of the same rupees.

Reducing Balance vs Flat Rate Interest: can one borrowing carry two true rates?

Yes, and the household's own loan carries both. A reducing balance rateA rate charged on what is still owed at each point, so the charge falls as the debt falls. A reducing balance rate prices the money the borrower actually has. asks a different question of exactly the same rupees. Instead of asking what percentage the total charge is of the original amount, it asks what monthly rate, applied to the balance as it actually stood in each of the thirty months, produces exactly Rs 12,500/- of charge and clears the loan on the thirtieth instalment.

Solve that and the answer is about 0.94 per cent a month, or about 11.3 per cent a year. Not one rupee has moved. The Rs 82,000/- is the same Rs 82,000/-, the thirty instalments are the same Rs 3,150/-, the charge is the same Rs 12,500/-. Only the question changed, and the answer nearly doubled.

6.10 per cent flat and about 11.3 per cent reducing describe the identical Rs 12,500/- on the identical Rs 82,000/-, and the second figure is 1.85 times the first. Neither is a trick and neither is a rounding. The two figures are honest measurements taken against two different reference amounts, in the same way that a journey can be described as thirty kilometres or as forty minutes without either description being false.

Why is the reducing balance figure always the larger of the two?

Because the household owed the full Rs 82,000/- for one month out of thirty. After that it owed less every single month, and by the end it owed almost nothing. A flat rate divides the charge by an amount the household stopped owing after the first instalment, so it is dividing by too big a number, so it produces too small a percentage. A reducing balance rate divides by what was actually being used. A reducing balance rate is the price of the money the household actually had.

Here is the exact hinge, and it is one line of arithmetic. Across those thirty months the average amount the household actually owed was Rs 44,282/-, a little over half of what it borrowed. And Rs 82,000/- divided by Rs 44,282/- is 1.85. The 1.85 is not a coincidence and it is not approximately the ratio between the two rates. The 1.85 is the ratio, exactly. The gap between a flat rate and a reducing balance rate is nothing more than the original amount divided by the average amount actually owed, so the reducing figure can never be the smaller of the two.

The same ratio shows in the instalments themselves. Every one of the thirty is Rs 3,150/-, but what is inside them keeps changing. The interest part is computed each month on what is still owed, and the rest goes to the debt. In the first month Rs 772/- of the Rs 3,150/- is interest. By the fifteenth it is Rs 438/-. In the thirtieth it is Rs 29/-. The instalment never moved; the composition moved all the way across.

Read the bottom row against the top one. Rs 94,500/- goes out, Rs 82,000/- of it is the borrowing coming back and Rs 12,500/- of it is the rent on time, and that Rs 12,500/- is the identical figure the flat rate called 6.10 per cent. The table is not a second borrowing. The table is the same borrowing, seen from inside. Amounts are rounded to the nearest rupee, so a row or two may differ by one rupee from a schedule computed to the paisa.

Push the control from six months to sixty and the shape of the answer is not the one most people predict. At six months the two figures sit 1.70 apart. By twenty four months they are 1.85 apart, and that is as far as they ever get. At thirty months, the household's own tenure, the ratio is still 1.85. Take it out to sixty and the ratio comes back down, to about 1.80. The gap is only ever the original amount divided by the average amount owed, and that ratio has a ceiling. So the gap widens fast out of the very short tenures, peaks near two years and then eases back across the rest of the range. What does not settle is the rupees: the charge climbs from Rs 2,720/- at six months to Rs 25,700/- at sixty. The flat quotation on that same unchanged contract barely moves by comparison, reading 6.09 per cent near two years and only 6.27 per cent at five. A flat figure can sit almost still while the price in rupees multiplies nearly ten times.

How Interest Changes the Cost of Borrowing: what does a longer tenure add?

Tenure is where rent on time stops being a metaphor. The rate is charged every month on whatever is still owed, and a longer tenure leaves more owed for longer, so under the household's contracted rate doubling the tenure slightly more than doubles the charge. Thirty months costs Rs 12,500/-. Sixty months costs Rs 25,700/-, a little over twice that. And the instalment moves in the opposite direction. The instalment is the figure a household actually feels each month.

Look at what that does to the two numbers side by side. A twelve month tenure on Rs 82,000/- means an instalment of Rs 7,258/- and a charge of Rs 5,096/-. A sixty month tenure means an instalment of Rs 1,795/- and a charge of Rs 25,700/-. The instalment falls to a quarter while the charge rises five times. Both of those things happen for one reason. The money is being rented for longer. Nothing has gone wrong in the second case. A longer tenure is not a worse deal in some moral sense. A longer tenure is a different purchase: less pressure per month, more rent in total.

For the Bhosale household this stopped being theoretical in year two. The market lane outside Ashok Bhosale's tailoring counter was dug up for drainage work and stayed dug up for five months, the counter took Rs 52,800/- across the year against Rs 96,000/- the year before, and the household ran a deficit of Rs 20,640/- without changing a single thing about how it spends. A household in that position is not choosing between tenures on a whiteboard. The choice is whether this month works, and the tenure question therefore deserves both columns in front of it rather than one.

Why does a monthly rate look small and behave large?

A card is the other half of this subject, and it behaves differently. There is no tenure. Nobody set an end date. The Bhosale household's card carries a contracted 3.5 per cent a month, charged on the whole balance once the card is not cleared in full. Three and a half sounds like a small number, and it is spoken like one. The instinct that turns it into a yearly figure is to multiply by twelve. Twelve times 3.5 is 42 per cent.

Multiplying by twelve is not stupid and it is not far wrong on a loan where the balance is falling. On a balance nobody is clearing, it understates. Take the household's card balance of Rs 48,594/- at 31 March of year two and leave it untouched for twelve months. Each month's charge is added to the balance, so the next month is charged on a bigger number. After twelve months the balance is Rs 73,429/-. The growth is Rs 24,835/- of interest on a Rs 48,594/- balance, more than half the balance again in one year.

Multiplying 3.5 by twelve gives Rs 20,409/-, the actual figure is Rs 24,835/-, and the missing Rs 4,426/- is compoundingInterest being charged on interest that has already been added to the balance, so each period is charged on a larger amount than the last.. Made properly comparable, 3.5 per cent a month is about 51.1 per cent a year rather than 42, and that is the number to hold beside a loan rate. How a balance goes on growing on its own interest over years rather than months is covered separately. One thing matters here. A monthly rate and a yearly rate are not comparable until one of them is converted, and multiplication is not the conversion.

How are two rates that are quoted differently compared?

Everything above collapses into a short routine, short enough to be usable standing at a counter with a form in hand and somebody waiting. Two questions, and one escape route if either answer does not arrive.

The first question is over what period. The second is charged on what, the original amount or what is still owed. If both answers arrive, the two rates can be converted into the same kind of number and compared. If either answer does not arrive, no conversion is possible and no comparison means anything, and at that point there is a figure that cannot be quoted two ways: the total repayable, and beside it the amount actually received.

Ask for the total repayable and the amount actually received. Those two figures already contain every rate, every period and every basis, and the entire question of which rate is which stops mattering. On the household's loan those two numbers are Rs 94,500/- and Rs 82,000/-. Nobody needs to know whether the quotation said 6.10 or 11.3 to see what that borrowing costs. The two figures are not a shortcut around understanding rates. They are the check that survives when the rates have been quoted in ways that cannot be lined up.

Where is a stated rate not the whole cost?

One last gap, and it is the reason the escape route above asks for two figures rather than one. A rate prices the money. A rate does not price everything attached to the money. A processing charge, a documentation charge or an insurance premium bundled into the arrangement can be taken out of the amount released rather than added to the instalment, and when that happens the rate on the paper does not move at all while the price of the borrowing does.

Work it on the household's own loan. Suppose a processing charge of Rs 1,200/- were deducted from the Rs 82,000/- before it reached the seller, so the household received Rs 80,800/- and still repaid thirty instalments of Rs 3,150/-. The quoted rate is untouched, still 6.10 per cent flat. But the household has rented Rs 80,800/- and is paying back Rs 94,500/-, and solved against the money it actually received the reducing rate is about 12.50 per cent a year rather than 11.29. A charge deducted before the money arrives raises the price of a borrowing without appearing in the rate, so the amount actually received belongs beside the total repayable in every comparison. The charges that sit beside interest are covered separately.

Who uses this difference, and how?

The difference is not only a household matter. A lender pricing a small borrowing works in reducing balance terms internally, matching what its own funding costs look like, and may quote flat externally to get the figure across a counter in ninety seconds. Both figures live in the same file and neither one is the marketing version of the other.

An instalment is a fact about a month and a rate is a fact about a year, so somebody assessing a household's borrowing capacity ignores the quoted rate almost entirely and works from the instalment against the income. On the Bhosale household in January of year two, with the two-wheeler loan still running, the instalments came to Rs 9,180/- a month against a net monthly income of Rs 44,200/-. The instalment against the income is the number that decides whether a month works, and no rate on any quotation would have said it.

A household needs only one habit out of all of this: read the total repayable and the amount actually received, and treat every quoted rate as a claim that has to say its period and its basis before it counts. The Bhosale household's loan was cleared in January of year two, on schedule, with the thirtieth instalment. The household paid the Rs 12,500/-, and both descriptions of that Rs 12,500/- were true the whole way through.

The Bhosale household, Meghna Bhosale and Ashok Bhosale are invented.
Educational material. Not advice on any investment, tax, budget or market position.