Loan Types Explained

There are two honest ways to do this, and which one is right depends on how the lender quoted the rate. The tool calls the choice Rate Convention, on the Assumptions tab.

Effective is the honest reading of a rate quoted per year: twelve months of r compound back to exactly the yearly figure. An 8.4% loan charges 0.674413% a month, not 0.7%.

Nominal is the honest reading of a rate quoted per month. Indonesian vehicle credit is sold as 0.9% a month and written up as 10.8% a year; compounding that back down would charge 0.857% and understate what the contract actually says. Every example on this page uses the convention its own Quick Start preset uses, and says which.

You pay the same amount every period, and that amount is sized so the debt lands exactly on zero at the end. Interest is charged on what you still owe, so as the balance falls the interest shrinks and a bigger slice of the same payment goes to the principal.

It is the yardstick every other structure on this page gets measured against, and in most of the world it is simply what "a loan" means.

If the rate is zero the formula collapses to PMT = P / n, which is what a genuine 0% plan looks like. The tool's Quick Start → Card preset is built on exactly that, three 0% instalment plans where the only cost is the conversion fee.

A $45,000 car, 10% down, over five years at 8.4%. The deposit is $4,500, so P = $40,500, n = 60, and at the effective convention r = (1.084)1/12 − 1 = 0.674413% a month.

The first payment is mostly interest, 40,500 × 0.674413% = $273.14, leaving $549.86 to come off the debt. By the last payment the interest is down to $5.51 and almost the whole $823.00 clears principal. The payment never changes. What changes is what it buys.

The same preset's 3yr loan scenario is the useful contrast: the instalment jumps to $1,270.86 but the interest falls to $5,250.97. A shorter term is a bigger payment and a smaller bill, every time.

Interest is worked out once, on the amount you first borrowed, and the same interest is charged every period for the whole term. Repaying the loan does not reduce it. You go on paying interest on money you handed back months ago.

It is the standard quote for vehicle credit across South-East Asia, where the offer is written as a rate per month, and it is the mechanics behind Murabaha cost-plus financing, where the lender adds a fixed margin to a cost price and splits the total into equal instalments.

Notice there is no (1 + r)n anywhere. Nothing compounds, nothing shrinks, and that simplicity is exactly why the quoted number is so misleading.

A motorbike costs Rp 35,000,000 with 20% down, financed over 36 months at 0.9% a month flat, written up as 10.8% a year. So P = Rp 28,000,000, n = 36 and r = 10.8% ÷ 12 = 0.9%, giving 28,000,000 × 0.009 = Rp 252,000 of interest every month on top of 28,000,000 ÷ 36 = Rp 777,778 of principal.

That is the whole lesson in two numbers. The preset's second scenario is the identical money on an ordinary declining-balance loan at the identical headline 10.8%: it costs Rp 914,034 a month and Rp 4,905,238 of interest. The flat quote costs Rp 4,166,762 more for the same bike, the same term and the same advertised rate.

A bank buys a machine for $50,000 and sells it to you for $60,000, payable in 48 equal instalments of $1,250. No interest rate is quoted at all, only a fixed $10,000 margin. That is a flat rate loan with P = 50,000, n = 48 and a flat 5% a year, because 50,000 × 5% × 4 years = 10,000. A margin is a per-period figure, so it reads as nominal, the same as the motorbike.

A 20% margin over four years sounds like 5% a year, and a borrower will compare it against a 5% bank loan. Priced properly it is 9.64%. The structure has not changed anything about the ethics of the product. It has changed the number you should be comparing.

For the first k periods you pay only the interest. None of it touches the principal, so the debt sits exactly where it started. After that the loan turns into an ordinary amortizing one, sized to clear the untouched balance over whatever term is left.

If k equals the full term the loan never amortises at all: you pay interest the whole way and hand back the entire principal on the last day.

The second line is the amortizing formula from card 01 with n − k in place of n. The same debt now has fewer periods to clear, so the payment jumps.

A $650,000 property with 20% down gives P = $520,000 over 30 years at 6.10%, so n = 360 and r = 0.494652% a month. Investors in Australia and New Zealand routinely take the first 5 years interest-only to keep early cash flow positive, which makes k = 60.

The preset's own 30-year loan, amortizing from day one, costs $3,096.24 a month and $594,645.74 of interest. The interest-only period saves $524.05 a month for five years, $31,443.00 in total, and costs $38,684.31 of extra interest over the life of the loan. You have not borrowed more cheaply. You have rented the same money for five years longer.

You borrow $80,000 at 10% for 12 months to cover a settlement gap, and repay the principal in one lump when your other property sells. Here k = n = 12 and r = 0.797414%.

With no principal ever repaid, the interest is simply P × r × n, the same expression as a flat rate loan. The difference is that here you really do keep the money the whole time, so the effective rate stays honest at 10.00% instead of nearly doubling.

The instalments are sized to pay the debt down to an agreed leftover amount, the residual, instead of down to zero. That residual falls due in one lump on the final day. You then refinance it, sell the asset to cover it, or pay it off.

The same structure carries a different name in every market, which is part of why it is hard to compare: a balloon in Australia, a Personal Contract Purchase in the British Isles, a guaranteed future value in dealer marketing everywhere.

Read it as the amortizing formula with a smaller principal. You take today's value of the residual out of the loan first, amortise only what is left, and hand the residual back at the end.

The same $45,000 car, now with a 35% residual. P = $40,500, n = 60, r = 0.674413%, and R = 40,500 × 35% = $14,175.

The trade is visible in one sentence: a residual buys you $192.45 a month for five years, $11,547.00 of breathing room, and costs $2,627.94 of extra interest plus a $14,175 bill on the last day. It is not a cheaper loan. It is a smaller loan with a debt parked at the end.

This is not a different shape of loan. It is the same arithmetic with a different unknown. A seller tells you the price and the monthly payment but never the rate, so you work the rate out from the payments instead of the payments from the rate.

It is the everyday shape of Buy Now Pay Later and of every "just $X a month" quote on a showroom floor. The payments do not even have to be level: a plan can step, and the method is the same.

There is no way to rearrange that into r = something, so it is found by trial. Guess a rate, run the whole schedule, see whether the last balance overshoots or undershoots zero, then halve your search range and guess again. Twenty or so rounds pin it to more decimals than money has. The tool does this for you and calls the answer the Implied Rate.

An $1,800 phone, offered as twelve payments of $150. Twelve times $150 is $1,800 exactly, the same as the cash price, so there is nothing extra to find. Run the balance forward and it lands on zero with r = 0.

This is what a real 0% plan looks like, and it is worth taking: you keep your $1,800 earning the risk-free rate for a year while the seller waits. The point of solving for the rate is not that every plan is a trap, it is that you cannot tell which is which by looking.

The same preset offers the same $1,800 phone as 24 payments of $82 or 36 payments of $57. Neither quotes a rate. Solve both and they land within a whisker of each other, a little over 9% a year, so the rate is not what separates them.

What separates them is time. At the same rate, the plan with the smallest instalment carries the biggest bill, because you keep the debt for three years instead of two. $57 a month feels like the kindest offer on the counter and costs $252, half as much again as the $82 plan's $168.

On the $57 plan, month one charges $13.07 of interest, so only $43.93 of your payment touches the phone. Nothing about any of these three offers was a lie. The rate was simply never quoted.

No instalments at all. Interest is added to the debt every period and then earns interest itself, and the whole thing is settled in a single payment at maturity.

Used where there is nothing to repay from until the project finishes or the asset sells. It is the only structure with no cash flow until the last day, which is exactly what makes it risky.

This is plain compound growth. It is the same formula a savings account uses, pointed the other way.

A block of land held for two years. You borrow $100,000 at 12% for 24 months and settle everything when the block sells. So P = 100,000, n = 24, r = 0.948879%.

An ordinary amortizing loan on the same $100,000 at the same 12% would cost $4,678.75 a month and only $12,290.02 of interest. The bullet costs $13,149.98 more, and every cent of that difference is the price of having the money the whole time instead of giving it back as you go.

You pay nothing for the first k periods, but interest still runs and is added to the debt. Normal instalments then start on a bigger balance with fewer periods left to clear it.

This is the only structure where the debt climbs above what you originally borrowed while you are still a good customer. Compare it with interest-only, card 03, where the interest is paid and so the balance merely stands still.

Card 06 for the holiday, then card 01 for the rest. Nothing new, just the two joined end to end.

Buy now, pay nothing for twelve months. A $6,000 fit-out financed at 19.9% over 36 months with the first 12 months free of payments. So n = 36, k = 12, r = 1.523894%.

The preset's second scenario is the same money on the same 36-month term at the same 19.9%, paid from day one: $217.78 a month and $1,840.02 of interest. The holiday moves $1,194.00 of interest into the debt, where it earns interest of its own, and squeezes the repayment into 24 months instead of 36. Twelve free months cost $803.61, which is about $67 a month of deferral.