Two quotes that look close but are not
Suppose you need 1,000,000 for five years. One offer says 10% flat. Another says 14% on a reducing balance. The first looks cheaper by four points. It is not.
| 10% flat | 14% reducing balance | |
|---|---|---|
| How interest is found | 1,000,000 × 10% × 5 years | Charged monthly on the balance still owed |
| Total interest | 500,000.00 | 396,095.05 |
| Monthly installment | 25,000.00 | 23,268.25 |
| Total repaid | 1,500,000.00 | 1,396,095.05 |
| Equivalent reducing-balance rate | 17.2737% | 14% |
The flat-rate loan costs 103,904.95 more and has a higher monthly installment. Flat-rate pricing appears in some vehicle financing and consumer installment offers, where the quote is a single percentage applied to the amount financed. Nothing about it is hidden, but the percentage is not comparable with a mortgage rate, a bank's reducing-balance personal-loan rate, or the rate in an APR disclosure.
How each method calculates interest
P is the amount financed, f is the flat annual rate as a decimal and t is the term in years. For 1,000,000 at 10% for 5 years: interest 500,000, installment 1,500,000 ÷ 60 = 25,000.
Interest each month is r times the balance still owed, so it shrinks as you repay. For 1,000,000 at 14% for 60 months the installment is 23,268.25, as the Loan Payment calculator confirms.
Under the flat method, interest is 500,000 ÷ 60 = 8,333.33 every month from first to last, though by the final installment you owe almost nothing. You are paying interest on money you have already returned. On a reducing balance, the same principal would have an average outstanding balance of roughly half the original amount over the term, which is why the equivalent rate is close to, but less than, double the flat rate.
You can see the gap in the first installment. Run 1,000,000 over 5 years at the equivalent 17.2737% through the Amortization calculator: the payment comes out at 25,000 (24,999.98 at that four-decimal rate), and month 1 is 14,394.75 interest and 10,605.23 principal. The flat schedule calls that same payment 8,333.33 interest and 16,666.67 principal. The cash is identical; only the label differs. On a reducing balance, interest falls each month as the balance falls, just as the amortization schedule guide describes, while the flat split stays the same for all 60 months. That is why the flat label understates the rate you are really paying.
Converting a flat rate with the Interest Rate calculator
The conversion has no neat closed formula, because the rate sits inside an exponent. Calculation Guide's Interest Rate calculator solves it numerically: give it the principal, the equal monthly installment and the term, and it finds the reducing-balance nominal annual rate that produces exactly that installment.
- Compute the flat installment: principal × (1 + flat rate × years) ÷ months. For the example, 1,000,000 × 1.5 ÷ 60 = 25,000.
- Enter principal 1,000,000, monthly payment 25,000 and term 5 years.
- Read the result: 17.2737%. That is the rate to compare with other reducing-balance quotes.
If a dealer quotes only an installment and a term, skip step 1 and enter the installment directly. That works for any equal-payment offer, flat or not, and is often the most honest way to compare: the installment and term are what you will actually pay.
Equivalent rates for common flat quotes
| Flat rate | 3-year term | 5-year term |
|---|---|---|
| 6% | 11.0825% | 10.8479% |
| 8% | 14.5481% | 14.1254% |
| 10% | 17.9177% | 17.2737% |
| 12% | 21.1999% | 20.3100% |
Across this table the equivalent rate is about 1.7 to 1.85 times the flat rate. The multiple is a little larger for shorter terms: 10% flat is 17.972% over one year, 17.2737% over five and 16.657% over seven. Do not use a fixed multiplier as a shortcut; solve the actual installment.
The converted figure is a nominal annual rate compounded monthly. If you want a figure that includes monthly compounding, see how nominal rates become an effective annual rate. And if the offer adds processing or documentation fees, the true cost is higher still, which is the distinction between an interest rate and an APR.
Early settlement is where the methods diverge again
A flat loan and its converted reducing-balance equivalent have identical installments, so over the full term they cost exactly the same. The difference reappears if you pay off early. A reducing-balance view of the 10% flat loan says you still owe 605,578.45 after 30 installments. A flat schedule that simply splits each 25,000 into 16,666.67 principal and 8,333.33 interest would say 500,000. Which figure a lender uses for the payoff amount, and whether it adds a settlement charge, is set by the contract. Ask for the early-settlement method in writing before you sign.
What the conversion does not settle
- Fees and add-ons. Insurance, registration, tracking devices and processing fees bundled into the installment raise the solved rate. Enter only the finance installment to isolate the rate, or the total installment to see the all-in figure.
- Balloon or residual payments. A large final payment breaks the equal-installment assumption, so the solved rate would be wrong.
- Islamic financing. Ijarah and murabaha offers are priced as rentals or sale markups, not interest. The conversion still measures the cost of the cash flows, but it does not describe the contract's structure or Shariah treatment.
- Down payments. Convert using the amount actually financed, not the vehicle's price.