Simple interest is charged only on the amount lent. Compound interest, chakravriddhi byaj or "byaj par byaj", adds unpaid interest to the principal at fixed dates, so interest starts earning interest. On ₹1,00,000 at ₹2 sekda for 5 years, simple interest is ₹1,20,000; added monthly, it becomes ₹2,28,103.
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What is simple interest (sadharan byaj)?
Simple interest, or sadharan byaj, is worked out on the principal alone. Interest that piles up is kept to one side as interest due. However long it stays unpaid, it never earns interest itself.
Simple interest = P × R × T ÷ 100
P is the principal, R the rate in % a year and T the time in years.
₹2 sekda means ₹2 a month on every ₹100: 2% a month, or 24% a year (what sekda means). So ₹1,00,000 for one year earns ₹1,00,000 × 24 × 1 ÷ 100 = ₹24,000. Every year adds the same amount, so after 5 years the interest is ₹1,20,000.
What is compound interest (chakravriddhi byaj)?
Compound interest is interest on interest. In a khata it works like this: on fixed dates, the unpaid interest is added to the principal, and from then on interest is charged on the bigger amount. Each of those dates is called a rest. A loan can have a monthly, quarterly, half-yearly or yearly rest.
Take ₹1,00,000 at ₹2 sekda with a yearly rest. In the first year the interest is ₹24,000, exactly as with simple interest. Then it is added to the principal, which becomes ₹1,24,000. In year two the interest is ₹29,760, not ₹24,000. The extra ₹5,760 is 24% of last year’s ₹24,000 of interest. That extra is the byaj par byaj.
A = P × (1 + R ÷ k)^(k × T)
A is the total at the end, P the principal, R the yearly rate as a decimal (24% = 0.24), k the number of rests in a year (12 monthly, 4 quarterly, 2 half-yearly, 1 yearly) and T the years. Compound interest = A − P. Every case of this formula, solved: compound interest formula.
With a monthly rest for one year: A = ₹1,00,000 × (1 + 0.24 ÷ 12)^12 = ₹1,00,000 × 1.02^12 = ₹1,26,824.18. The interest is ₹26,824.18, against ₹24,000 at simple interest.
Difference between simple and compound interest
| Point | Simple interest | Compound interest |
|---|---|---|
| Meaning | Interest on the principal only | Interest on the principal plus interest already added to it |
| Charged on | The same principal every time | A principal that grows at every rest |
| Formula | P × R × T ÷ 100 | P × (1 + R ÷ 100)^T − P (yearly rest) |
| Interest each year | Same every year: ₹24,000 | Grows each year: ₹24,000, ₹29,760, ₹36,902.40 (yearly rest) |
| Growth over time | A straight line | A curve that bends upwards |
| Total after 5 years | ₹2,20,000 | ₹2,93,163 yearly rest, ₹3,28,103 monthly rest |
| Real yearly rate | The quoted rate: 24% | Higher if added more than once a year: 26.82% if added monthly |
| Who gains | The borrower | The lender or saver |
| When they are equal | Always the same each year | Equal until the first rest, or if interest is paid at every rest |
| Usual use in India | Most private sekda loans | Savings accounts, FDs paid at maturity, unpaid loan interest |
Simple vs compound interest on ₹1,00,000 at ₹2 sekda, year by year
Here is the same loan with nothing paid back, worked out by our calculator for every year up to 10. Read down the columns and you can see the two shapes: simple interest adds the same ₹24,000 every year, while compound interest adds more each year.
| Time | Simple interest | Yearly rest | Monthly rest | Extra with a monthly rest |
|---|---|---|---|---|
| 1 year | ₹1,24,000 | ₹1,24,000 | ₹1,26,824 | ₹2,824 |
| 2 years | ₹1,48,000 | ₹1,53,760 | ₹1,60,844 | ₹12,844 |
| 3 years | ₹1,72,000 | ₹1,90,662 | ₹2,03,989 | ₹31,989 |
| 4 years | ₹1,96,000 | ₹2,36,421 | ₹2,58,707 | ₹62,707 |
| 5 years | ₹2,20,000 | ₹2,93,163 | ₹3,28,103 | ₹1,08,103 |
| 6 years | ₹2,44,000 | ₹3,63,522 | ₹4,16,114 | ₹1,72,114 |
| 7 years | ₹2,68,000 | ₹4,50,767 | ₹5,27,733 | ₹2,59,733 |
| 8 years | ₹2,92,000 | ₹5,58,951 | ₹6,69,293 | ₹3,77,293 |
| 9 years | ₹3,16,000 | ₹6,93,099 | ₹8,48,826 | ₹5,32,826 |
| 10 years | ₹3,40,000 | ₹8,59,443 | ₹10,76,516 | ₹7,36,516 |
In the first year a yearly rest changes nothing, because no interest has been added yet. After that the gap grows quickly. By year 5, a monthly rest costs ₹1,08,103 more than simple interest: 90% on top of the simple interest itself. By year 10 the monthly-rest total is 3.2 times the simple-interest total.
Try it in the calculatorTry it: ₹1,00,000 at ₹2 sekda, added monthly, for 5 yearsDifference between CI and SI for 2 and 3 years (formula)
With a yearly rest, compound and simple interest are equal for the first year. In year two, compound interest also charges interest on the first year’s interest, and that is the whole difference. So there are two shortcuts:
CI − SI for 2 years = P × (R ÷ 100)²
CI − SI for 3 years = P × (R ÷ 100)² × (3 + R ÷ 100)
Exam questions often run it backwards: "The difference between CI and SI for 2 years at 6% is ₹63. Find the sum." Divide by (R ÷ 100)²: 63 ÷ 0.0036 = ₹17,500.
The shortcuts assume a yearly rest. With half-yearly interest, use half the rate and count half-years: for 1 year at 10% added half-yearly, CI − SI = ₹10,000 × (5 ÷ 100)² = ₹25. For quarterly or monthly interest, work out the full compound amount instead.
Try it in the calculatorCheck it: ₹10,000 at 10%, added yearly, for 3 yearsMonthly, quarterly or yearly: does it matter how often interest is added?
Yes. The more often unpaid interest joins the principal, the faster the total grows. At the same ₹2 sekda, a monthly rest beats quarterly, quarterly beats half-yearly, and half-yearly beats yearly.
| Interest added | Interest in 1 year | Yearly rate in effect | Total after 5 years |
|---|---|---|---|
| Simple (never added) | ₹24,000 | 24% | ₹2,20,000 |
| Yearly | ₹24,000 | 24% | ₹2,93,163 |
| Half-yearly | ₹25,440 | 25.44% | ₹3,10,585 |
| Quarterly | ₹26,247.70 | 26.25% | ₹3,20,714 |
| Monthly | ₹26,824.18 | 26.82% | ₹3,28,103 |
So "₹2 sekda, added monthly" really costs 26.82% in the first year, not 24%. Over 5 years a monthly rest adds ₹34,940 more than a yearly rest on the same loan. When you agree a loan, ask how often interest will be added, not just the rate. The rate converter turns sekda into a yearly rate.
Rule of 72: how fast money doubles
Divide 72 by the yearly rate to see roughly how long compound interest takes to double money: at ₹2 sekda (24%), 72 ÷ 24 = 3 years, and with a yearly rest it really takes 3 years 2 months 14 days. At simple interest it takes 100 ÷ 24, or 4 years 2 months. The money double calculator gives the exact time for any rate.
Where do you meet simple and compound interest in India?
| Where | Simple or compound | How often, and the catch |
|---|---|---|
| Savings account | Compound | RBI rules make banks credit interest at least every quarter |
| Bank FD paid at maturity | Compound | Usually added every quarter: 7% becomes 7.19% a year |
| FD that pays out interest | Works like simple | The interest leaves the deposit, so it earns nothing more |
| Bank loan on EMIs (home, car, personal) | Worked out monthly | Interest at monthly rests (RBI); on-time EMIs leave nothing to compound |
| Overdraft or missed EMI | Compound | Unpaid interest can join the balance; penal charges cannot earn interest |
| Credit card | Compound, generally | Unpaid interest becomes part of next month’s balance; card terms vary |
| Private sekda loan | Usually simple | Compound only if agreed, for example a yearly rest |
| Late payment to a micro or small business | Compound | Monthly rests under the MSMED Act |
Some state money-lending laws limit compound interest. Maharashtra’s 2014 money-lending law, for example, does not allow money-lenders to charge it.
How to keep byaj par byaj from hurting
- Pay the interest at each rest. If interest is cleared every time it falls due, there is nothing to add to the principal, and compound interest costs the same as simple interest.
- Agree the terms in writing. Write down the rate (for example ₹2 sekda), whether interest is simple or compound, and how often it is added.
- Check the numbers. Put the amount, rate and dates into our compound interest calculator or byaj calculator and choose how often interest is added. Both show every step of the working.
7 short answersSimple vs compound interest: quick answers
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What is the difference between simple and compound interest?
Simple interest is charged only on the principal; compound interest is also charged on interest already added to the principal. Simple interest = P × R × T ÷ 100. Compound interest with a yearly rest = P × (1 + R ÷ 100)^T − P. On ₹1,00,000 at ₹2 sekda for 3 years, simple interest is ₹72,000; a yearly rest makes it ₹90,662.40 and a monthly rest ₹1,03,988.71.
What is the difference between CI and SI for 2 years and 3 years?
With a yearly rest, CI − SI = P × (R ÷ 100)² for 2 years and P × (R ÷ 100)² × (3 + R ÷ 100) for 3 years. On ₹1,00,000 at 24% (₹2 sekda), the gap after 2 years is ₹5,760: just 24% interest on the first year’s ₹24,000 of interest. After 3 years it grows to ₹18,662.40.
Which is better, simple or compound interest?
It depends on your side of the deal: a borrower pays less with simple interest, while a lender or saver earns more with compound interest. At the same rate the two are equal until the first rest, then compound pulls ahead. Leave ₹1,00,000 unpaid for 5 years at ₹2 sekda and the interest is ₹1,20,000 simple, ₹1,93,163 with a yearly rest and ₹2,28,103 with a monthly rest.
Do banks charge simple or compound interest on loans?
Banks work out loan interest every month on what you owe: RBI directions require monthly rests, except on some farm loans. On an EMI loan, each EMI pays that month’s interest first, so on-time EMIs leave no interest to compound. Unpaid interest, as in an overdraft or after a missed EMI, can be added to the balance and earn interest. Penal charges for late payment, though, cannot earn interest.
Do bank deposits earn simple or compound interest?
Mostly compound. RBI rules make banks credit savings-account interest at least every quarter, and once credited it earns interest too. FDs that pay out at maturity usually add interest every quarter. An FD that sends you its interest each month or quarter works like simple interest, because the interest leaves the deposit. A bank that advertises a compounded yield must also show the simple yearly rate.
Is compound interest legal in India?
It can be, within limits. RBI lets banks and NBFCs compound interest in the normal way. Private money-lending is regulated state by state: Maharashtra’s 2014 law, for one, bars money-lenders from taking compound interest. And under the Usurious Loans Act, 1918, a court deciding whether interest is excessive looks at whether it was compounded and how often.
How is compound interest worked out for months and days?
Interest is compounded at each full rest, and the months and days left over get simple interest on the new principal, much as banks treat a part quarter on an FD. ₹1,00,000 at ₹2 sekda with a yearly rest grows to ₹1,53,760 in 2 years; the next 4 months 15 days add ₹13,838.40, making ₹1,67,598.40 after 2 years 4 months 15 days. The compound interest calculator does this between any two dates.