Flat rate vs reducing balance interest: why 8 percent flat is not 8 percent

Two ways to quote the same loan

With reducing-balance interest, each month's interest is charged only on the principal still owed. As you repay, the base shrinks and so does the interest. This is how standard home loans and most bank loans are quoted, and it is the basis of the EMI formula.

With flat-rate interest, interest is charged on the original loan amount for the whole term, regardless of how much you have already repaid. The total interest is simply principal x flat rate x years. It is then added to the principal and divided by the number of months to give an instalment. Flat rates are common in some vehicle loans, consumer durable finance and certain personal loans. The arithmetic is easy for the seller to quote, but it hides the true cost.

Flat interest ignores the fact that you are repaying principal every month.

Worked example: 1,00,000 for 3 years at 8 percent flat

Borrow 1,00,000 for 3 years (36 months) at 8 percent flat. Interest is 1,00,000 x 8% x 3 = 24,000. The total to repay is 1,24,000, so the monthly instalment is 1,24,000 / 36 = 3,444.44.

Compare this with 8 percent on a reducing balance. For the same loan, the EMI formula gives 3,133.64 a month, a total of 1,12,810.92 and interest of 12,810.92. So at the same headline number, the flat loan costs 24,000 in interest, versus 12,810.92, which is 11,189.08 more, or about 87 percent more interest.

Why the flat rate is misleading

Think about what you actually owe. In month 1 you owe nearly the full 1,00,000. By month 18 you have repaid about half of it, yet the flat method still charges interest as if you owed all of it. At the end, in month 36, you owe almost nothing, but you are still paying the same interest component. On average over the loan you are borrowing roughly half the original amount, so you pay a rate of about double the headline on the average balance.

A simple picture helps. Imagine repaying a loan in equal principal slices of 2,777.78 a month over 36 months (100000 divided by 36). Your outstanding balance starts near 1,00,000 and ends near zero, so the average balance is close to half the loan, roughly 50,000. The flat method nevertheless charges 24,000 of interest, which is 24,000 / 3 years / 50,000, or about 16 percent a year on that average balance. That is the intuition behind the effective rate being close to double the headline flat rate.

There is a quick rule of thumb: the equivalent reducing rate is approximately 2n/(n+1) times the flat rate, where n is the number of monthly instalments. With n = 36 and a flat rate of 8 percent, that gives about 15.57 percent. It is only an approximation; the exact figure requires solving for the rate.

The exact effective rate (IRR)

To compare fairly, convert the flat loan into the rate that a reducing-balance loan would need in order to produce the same instalments. That is the internal rate of return (IRR) of the cash flows: you receive 1,00,000 now and pay 3,444.44 for 36 months. The monthly rate that makes the present value of those payments equal 1,00,000 is the solution of the EMI formula for r, which has no simple closed form and is found numerically. A script solving it gives a monthly rate of about 1.2123 percent.

Multiplying by 12 gives a nominal annual rate of about 14.55 percent. If you compound that monthly rate over a year, the effective annual rate is about 15.56 percent. So 8 percent flat corresponds to roughly 14.5 percent as a nominal reducing-balance rate. Check it: at 14.548 percent nominal, the EMI formula returns 3,444.44 for a 1,00,000, 36-month loan.

In this example, 8 percent flat is equivalent to about 14.55 percent nominal on a reducing balance.

Why the gap grows with tenure and rate

The longer the loan, the more principal is repaid early relative to the end, so the flat method overcharges more in effective terms. At very short terms the gap is smaller; at long terms the approximation 2n/(n+1) approaches double the flat rate. A higher flat rate also increases the gap in absolute terms. This is why flat rates are most misleading on multi-year loans.

How to compare loan offers fairly

A few practical habits protect you from comparing the wrong numbers.

• Ask whether the quoted rate is flat or reducing. If the answer is not clear in writing, ask again.
• Convert any flat rate to its reducing equivalent before comparing, using the Flat vs Reducing Interest Calculator.
• Compare the total amount repaid, not only the instalment.
• Include processing fees, insurance and prepayment charges. A lower rate with a high fee can cost more. Many loans quote an annual percentage rate (APR) or effective rate that includes fees; if offered, use it.
• Ask for the repayment schedule, and check that the first month's interest roughly equals balance x rate / 12.
• Remember that foreclosure or prepayment on a flat-rate loan may not reduce interest proportionally. Read the terms.

Using the tools

The Flat vs Reducing Interest Calculator converts a flat rate to the equivalent reducing-balance rate and compares EMIs and total interest side by side. Enter 1,00,000, 8 percent and 3 years to reproduce the figures above. Use the EMI Calculator to check what a reducing rate would cost, and the Loan Comparison Calculator to set two real offers next to each other. Small differences from rounding are normal, and your lender's schedule is the authority.

Frequently asked questions

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