How this calculator works
Every loan hides a rate. If you know what you borrowed and what you pay back, the rate is the one figure that makes the two match: here, 8.69% a year.
- Step 1You borrow₹10 lakhthe amount you received
- Step 2You pay each month₹12,500for 10 years
- Step 3One rate fits8.69%a year, compounded monthly
There is no tidy formula that gives the rate directly. The calculator tries rates between 0% and 1,200% a year and keeps halving the range until the loan balance after the last payment is exactly the balloon amount, or zero if there is none.
For growth, a direct formula exists. The ratio of the ending value to the starting value is raised to the power of one over the years, and one is taken away.
Nominal and effective rates
- Nominal annual rate8.69%The monthly rate multiplied by 12. This is how lenders usually quote a rate.
- Effective annual rate9.04%What the interest adds up to over a full year once each month’s interest earns interest too.
What the result leaves out
- Fees and chargesProcessing fees, insurance and other costs change what a loan really costs. They are not part of the payment you enter here.
- TaxesTax on interest earned, or tax relief on interest paid, is not modelled.
- Uneven cash flowsPayments are equal and monthly, with one optional balloon. Missed, early or changing payments need a different method.
Worked example
- The rate must satisfy
P = M × (1 − (1 + i)^−n) ÷ i + B × (1 + i)^−n- Nominal annual rate
12 × i- Effective annual rate
(1 + i)^12 − 1
- Ploan amount ₹10,00,000
- Mmonthly payment ₹12,500
- nnumber of payments 120
- Bballoon payment ₹0
- Total of all paymentsM × n + B₹15,00,000
- Total interest paidtotal paid − P₹5,00,000
- Monthly rate foundthe i that solves the equation0.724%
- Balance after the last paymentchecked month by month at this rate₹0
- Nominal annual rate12 × i8.69%
- Effective annual rate(1 + i)^12 − 19.04%
Growth works the same way, with no monthly payments. Here the ratio is the ending value divided by the starting value.
- Effective annual rate
(end ÷ start)^(1 ÷ years) − 1- Nominal annual rate
12 × ((1 + effective)^(1 ÷ 12) − 1)
- Growth ratioend ÷ start2.50 times
- Gain over the periodend − start₹1,50,000
- Effective annual rateratio^(1 ÷ years) − 112.14%
- Nominal rate, monthly compounding12 × monthly rate11.51%
Reading your result
The rate comes from your figures alone. It says what the money cost or earned, not whether that was a good deal.
- Nominal rate, payments only
- Nominal rate, payments plus balloon
If the payments add up to less than the loan amount, no rate of 0% or more fits. Check the figures, or add the balloon that is due at the end.
Comparing loan offers
Two loans with the same headline rate can cost different amounts once fees, rate type and term are counted.
If a lender quotes a flat rate, convert it with the flat vs reducing rate calculator before comparing. The APR calculator folds upfront fees into a single yearly rate.
Once you know the rate, the EMI calculator gives the payment for any term. For an investment’s growth rate from its start and end values, the CAGR calculator gives the same answer as growth mode here.
Common mistakes
Mistake: Entering a payment that includes insurance or other add-ons.
Instead: Use only the part of the payment that repays the loan, or accept a higher result.
Mistake: Comparing a nominal rate with an effective rate.
Instead: Compare nominal with nominal, or effective with effective.
Mistake: Entering months as years in the growth mode.
Instead: Divide months by 12: 18 months is 1.5 years.
Mistake: Using the growth mode when money was added along the way.
Instead: Use a tool built for regular deposits, since extra deposits change the rate.
This calculator estimates a rate from the figures you enter. It does not assess a loan, an investment or a lender. Check a lender’s written terms for the exact rate and charges, and consult a qualified professional about your circumstances.
Checking the method
A separate script re-solves every test rate two ways, with a month-by-month ledger and with the closed-form equation, and must agree to a billionth of a percent.
Read how we test our calculators, or browse more money calculators.