Finance
Interest Rate Calculator
Solves for the rate, where the result depends on which rate is meant.
Result
Solved by iteration on a standard amortising schedule. It reflects the interest rate only, if the deal also carries fees, the APR calculator gives the fuller comparison.
Get a Free Business AuditHow the calculation works
Given the other terms, the rate implied by a payment, a balance and a term is solved iteratively since there is no closed form. The result is a periodic rate which annualises differently depending on whether compounding is included, which is the distinction between a nominal annual rate and an effective one.
What moves the number
- Payment, principal and term.
- Payment frequency.
- Whether the annualised figure includes compounding.
- Fees, which the implied rate may or may not capture.
Where this one goes wrong
A nominal annual rate is the periodic rate multiplied by the number of periods, while the effective annual rate accounts for compounding within the year and is higher, which means the same arrangement can be quoted two ways and both be accurate. Establish which is being quoted. Where fees are involved, the rate implied by the payments alone understates the cost, and the APR is the figure that captures them.
Before you quote
- Establish whether a quoted rate is nominal or effective.
- Match the periodic rate to the payment frequency.
- Use APR where fees are involved.
Questions
About this calculator
Why do two quoted rates differ for the same arrangement?
Because a nominal annual rate multiplies the periodic rate by the number of periods while an effective annual rate accounts for compounding within the year. The effective figure is higher, and both can be accurate.
Can the rate be solved directly?
Not in closed form from a payment, principal and term, so it is solved iteratively. That is a computational detail rather than a limitation, and the result is as exact as the inputs are.
Does the implied rate include fees?
Only if the fees were in the amounts used. A rate implied by payments against the principal received understates the cost where fees were charged separately, which is what APR is designed to capture.
Put this calculator on your site
Free to embed. Paste this where you want it to appear. It stays up to date automatically because it loads from BDEVY.
Please keep the attribution line. It is the only thing we ask in return.
How to use this calculator
- Amount borrowed ($). Enter your own figure; the page starts at $20,000.
- Monthly payment ($). Enter your own figure; the page starts at $425.
- Term in years. Enter your own figure; the page starts at 5.
The result updates as you type, so you can try a figure, see what it does to implied annual rate, and change it back. Nothing you enter is sent anywhere or saved.
A worked example
These are the figures the calculator opens with. Every number in the results column below is produced by the same calculation the page runs, so you can follow it through before putting your own figures in.
What goes in
| Input | Value |
|---|---|
| Amount borrowed | $20,000 |
| Monthly payment | $425 |
| Term in years | 5 |
What comes out
| Result | Value |
|---|---|
| Implied annual rate main result | 10.01% |
| Total repaid | $25,500 |
| Total interest | $5,500 |
| Monthly rate | 0.83% |
Those terms imply an interest rate of 10.01% a year. You repay $25,500 in total, of which $5,500 is interest.
How sensitive the answer is
Holding everything else steady and changing only amount borrowed, this is what happens to implied annual rate. It is worth knowing which of your inputs the answer actually hinges on, and which barely move it.
| Amount borrowed ($) | Implied annual rate |
|---|---|
| $10,000 | 45.54% |
| $15,000 | 23.25% |
| $20,000 example above | 10.01% |
| $30,000 | 0.00% |
| $40,000 | 0.00% |
Every other input is held at the example value while this one changes, which is not how a real job behaves. Treat it as a guide to which number matters most, not as five separate quotes.
What each figure means
- Amount borrowed ($)
- A money amount, starting at $20,000.
- Monthly payment ($)
- A money amount, starting at $425.
- Term in years
- A number, between 0 and 50, starting at 5.
What the results tell you
| Result | What it is |
|---|---|
| Implied annual rate | The headline result. A percentage. |
| Total repaid | A money figure. |
| Total interest | A money figure. |
| Monthly rate | A percentage. |
Rates and terms move
Loan and interest figures assume the rate and term you enter hold for the whole period. Variable rates, fees rolled into the balance and early-repayment terms all change the real cost.
Keep going
Related calculators
APR Calculator
Works APR, which includes certain fees and is therefore the comparable figure.
Open calculatorLoan Calculator
Works a loan payment, where the term changes the total far more than it changes the payment.
Open calculatorPayment Calculator
Works a periodic payment, where the frequency affects the total.
Open calculatorNumbers are only half the job
Good margins still need customers finding you and systems that hold it together. BDEVY covers the marketing, technology and automation side.