To find the rate of interest, divide the byaj by the principal and the time, then multiply by 100. ₹3,000 byaj on ₹50,000 for 3 months: 3,000 × 100 ÷ (50,000 × 3) = ₹2 sekda a month, or 24% a year. Pick what to find below, or enter two amounts.
How to find the rate of interest (byaj dar kaise nikale)
The rate is the byaj on every ₹100 for one unit of time. Use the time in months to get the rate in ₹ sekda (₹ per ₹100 a month), or in years to get % a year. Sekda × 12 = % a year.
Rate = Byaj × 100 ÷ (Principal × Time)
Time in months gives ₹ sekda (% a month). Time in years gives % a year.
Simple interest formulas: byaj, rate, principal and time
All of these come from one formula. Know any three of byaj, principal, rate and time, and the fourth follows. In Hindi they are often written with मूलधन (P), दर (R), समय (T) and मिश्रधन (A).
Byaj (I) = P × R × T ÷ 100
Rate (R) = I × 100 ÷ (P × T)
Principal (P) = I × 100 ÷ (R × T)
Time (T) = I × 100 ÷ (P × R)
Mishradhan (A) = P + I, so P = A × 100 ÷ (100 + R × T)
Use this when you know the total returned, not the byaj alone.
Mooldhan, mishradhan, byaj dar: the words in English
| Word | In English | What it means | Example |
|---|---|---|---|
| मूलधन (mooldhan) | Principal (P) | The money lent or borrowed | ₹50,000 |
| ब्याज (byaj, sood) | Interest (I) | What is paid for using the money | ₹3,000 |
| मिश्रधन (mishradhan) | Amount (A) | Principal + byaj: the total to return | ₹53,000 |
| ब्याज दर (byaj dar) | Rate of interest (R) | Byaj on ₹100 for a month or a year | ₹2 sekda = 24% a year |
| समय (samay) | Time (T) | How long the money was out | 3 months |
| सैकड़ा (sekda, saikda) | Per hundred | ₹ on every ₹100 each month | ₹2 sekda = ₹2 per ₹100 a month |
| टका (taka) | Rupee (old word) | "2 taka byaj" is read as ₹2 sekda | ₹2 on ₹100 a month |
How to find the principal (mooldhan kaise nikale)
From the byaj
₹4,500 of byaj at ₹1.5 sekda for 6 months came from a principal of 4,500 × 100 ÷ (1.5 × 6) = ₹50,000.
From the total (mishradhan se mooldhan)
If ₹54,500 was returned in all at the same rate and time, the principal is 54,500 × 100 ÷ (100 + 1.5 × 6) = 54,500 × 100 ÷ 109 = ₹50,000, and the byaj is ₹54,500 − ₹50,000 = ₹4,500.
Try it in the calculatorFind the principal behind a total of ₹54,500How to find the time (samay kaise nikale)
₹50,000 at ₹2 sekda earned ₹5,000 of byaj in 5,000 × 100 ÷ (50,000 × 2) = 5 months. With a monthly rate the answer comes out in months; multiply any part month by 30 for days. ₹2,500 of byaj took 2.5 months, that is 2 months 15 days.
The school-book version uses % a year and gives years: ₹200 on ₹1,000 at 10% a year took 200 × 100 ÷ (1,000 × 10) = 2 years.
Try it in the calculatorFind the time for ₹2,500 of byaj on ₹50,000Rate from two amounts: what rate turned ₹50,000 into ₹65,000?
Say ₹50,000 was lent and ₹65,000 came back after 1 year 2 months (14 months). The byaj is ₹15,000. As simple interest that is 15,000 × 100 ÷ (50,000 × 14) = ₹2.14 sekda, or 25.71% a year.
| Byaj added to principal | % a year | ₹ sekda |
|---|---|---|
| Never (simple interest) | 25.71% | ₹2.14 |
| Every year | 24.83% | ₹2.07 |
| Every 3 months | 23.1% | ₹1.93 |
| Every month | 22.7% | ₹1.89 |
The more often byaj is added to the principal, the lower the rate that produces the same ₹65,000. The yearly figure treats the last 2 months as simple interest, as our calculators and most lenders do. The plain CAGR formula, which compounds the part year too, gives 25.22%.
Over whole years the yearly figure is the CAGR. ₹1,00,000 growing to ₹1,76,234.17 in 5 years is 12% a year with byaj added yearly, but 15.25% a year as simple interest. For the other way round, see the compound interest calculator.
Try it in the calculatorFind the rate: ₹50,000 lent, ₹65,000 back after 14 monthsMistakes that give the wrong rate
- Mixing units. A monthly rate with years (or a yearly rate with months) is off by 12 times.
- Using the total as the byaj. Take the principal off the total first: byaj = mishradhan − mooldhan.
- Counting days loosely. A bahi counts whole calendar months, then days at 1/30 of a month; banks count actual days ÷ 365. See the interest per day calculator.
- Not asking "a month or a year?" "2%" from a lender usually means 2% a month (₹2 sekda, 24% a year). See what rupaye sekda means.
- Using it on an EMI loan. EMIs repay principal every month, so this formula understates the rate. Use the EMI calculator.
7 short answersByaj dar, mooldhan and samay: quick answers
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How do I calculate the interest rate per month in rupees?
Divide one month’s byaj by the principal and multiply by 100. That is the rate in rupees per ₹100 a month (sekda). ₹3,000 of byaj on ₹50,000 over 3 months is ₹1,000 a month, and 1,000 ÷ 50,000 × 100 = ₹2 sekda, which is 24% a year.
What are mooldhan and mishradhan in English?
Mooldhan (मूलधन) is the principal: the money first lent or borrowed. Mishradhan (मिश्रधन) is the amount: principal plus interest, the total to be returned. With ₹3,000 of byaj on ₹50,000, the mooldhan is ₹50,000 and the mishradhan is ₹53,000. Byaj dar is the rate and samay is the time.
How do I find the principal from the total amount?
Principal = total × 100 ÷ (100 + rate × time). If ₹54,500 was returned after 6 months at ₹1.5 sekda, the principal is 54,500 × 100 ÷ 109 = ₹50,000, and the rest, ₹4,500, is byaj. Keep the rate and time in the same unit: sekda with months, % a year with years.
How do I find the time in simple interest?
Time = byaj × 100 ÷ (principal × rate). With a monthly rate the answer is in months: ₹5,000 of byaj on ₹50,000 at ₹2 sekda took 5,000 × 100 ÷ (50,000 × 2) = 5 months. Multiply a part month by 30 for days: 2.5 months is 2 months 15 days.
I lent ₹50,000 and got back ₹65,000 after 14 months. What rate is that?
As simple interest, ₹2.14 sekda, or 25.71% a year: the ₹15,000 of byaj ÷ ₹50,000 ÷ 14 months × 100. If byaj was added to the principal every year, the same growth is 24.83% a year; every month, 22.7%. Choose "Rate from two amounts" in the calculator above.
Is CAGR the same as the interest rate?
CAGR is the yearly compound rate that turns the first amount into the last: (final ÷ start) raised to 1 ÷ years, minus 1. Over whole years it equals the rate with byaj added once a year. ₹1,00,000 growing to ₹1,76,234.17 in 5 years is a CAGR of 12%; as simple interest the same growth is 15.25% a year.
How do I find the interest rate of an EMI loan?
Not with the simple interest formula. Each EMI returns part of the principal, so dividing the total interest by the full loan and the years gives a rate well below what the bank charges. The EMI calculator finds the real reducing rate from the loan amount, the EMI and the number of months.
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