The compound interest formula is A = P × (1 + R/100)^n, and compound interest = A − P. ₹10,000 at 10% a year for 2 years: A = 10,000 × 1.1² = ₹12,100, so the interest is ₹2,100. For half-yearly, quarterly or monthly interest, divide R by 2, 4 or 12 and multiply n by the same number.
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The compound interest formula
A = P × (1 + R ÷ 100)^n; CI = A − P
A is the amount at the end (principal + interest), P the principal, R the rate in % a year and n the number of years. This is for interest added once a year.
Each year the amount is multiplied by (1 + R ÷ 100), because the interest is added to the principal and earns interest from then on. Multiply n times and you get the power n.
Try it in the calculator₹10,000 at 10%, added yearly, for 2 yearsSchool notation and finance notation: the same formula
School books write the formula with R in percent and n in years or periods. Finance books and bank websites write A = P(1 + r/n)^(nt). They give the same answer. The trap is the letter n, which means different things in the two.
| What it is | School (NCERT style) | Finance books |
|---|---|---|
| Amount at the end | A | A |
| Principal | P | P |
| Yearly rate | R, in percent (10) | r, as a decimal (0.10) |
| Times interest is added in a year | built into R and n | n (4 for quarterly) |
| Time | n = years (or periods) | t = years |
| Yearly | A = P(1 + R/100)^n | A = P(1 + r)^t |
| Quarterly | A = P(1 + R/400)^(4n) | A = P(1 + r/4)^(4t) |
Half-yearly, quarterly and monthly compound interest formula
When interest is added more than once a year, use the rate for one period and count the periods: half-yearly R ÷ 2 for 2n half-years, quarterly R ÷ 4 for 4n quarters, monthly R ÷ 12 for 12n months.
Half-yearly: A = P × (1 + R ÷ 200)^(2n)
Quarterly: A = P × (1 + R ÷ 400)^(4n)
Monthly: A = P × (1 + R ÷ 1200)^(12n)
The more often interest is added, the more you end with. Here is ₹50,000 at ₹2 sekda (24% a year) for one year, each way:
| Interest added | Rate × periods | Working | Amount | A year really earns |
|---|---|---|---|---|
| Yearly | 24% × 1 | 50,000 × 1.24^1 | ₹62,000 | 24% |
| Half-yearly | 12% × 2 | 50,000 × 1.12^2 | ₹62,720 | 25.44% |
| Quarterly | 6% × 4 | 50,000 × 1.06^4 | ₹63,123.85 | 26.25% |
| Monthly | 2% × 12 | 50,000 × 1.02^12 | ₹63,412.09 | 26.82% |
So 24% added monthly gives ₹63,412.09, as if the rate were 26.82% added once a year. This "effective" rate is how to compare offers that add interest at different times.
Compound interest when time is in a fraction: 2 years 4 months
For 2 years 4 months there are two ways to work it out, and sources differ on which to use:
- Whole years, then simple interest for the rest. Compound the whole years, then add simple interest on the new amount for the part year: A = P × (1 + R/100)^2 × (1 + R/100 × 4/12). This is the usual exam method, and it is how banks treat a part quarter on an FD. Our calculator works this way.
- A fractional power. A = P × (1 + R/100)^(2⅓). It treats the part year as compound too, and gives a little less.
Different rates in different years
A = P × (1 + R₁ ÷ 100) × (1 + R₂ ÷ 100) × …
Multiply by one bracket for each year, each with that year’s rate.
How to find the rate in compound interest
R = 100 × [(A ÷ P)^(1/n) − 1]
For interest added yearly. Take the n-th root of A ÷ P, subtract 1 and multiply by 100.
If the same money grew at simple interest, the rate is (A − P) ÷ P ÷ years × 100 instead. The byaj dar calculator works out the rate, principal or time for you.
How to find the time in compound interest
n = log(A ÷ P) ÷ log(1 + R ÷ 100)
Any log works (common or natural), as long as you use the same one on top and bottom.
How to find the principal in compound interest
P = A ÷ (1 + R ÷ 100)^n
If the interest is given instead of the amount: P = CI ÷ [(1 + R ÷ 100)^n − 1].
Compound interest table: what ₹100 becomes
Each cell is (1 + R/100)^n × 100, with interest added yearly. Multiply by your amount ÷ 100: for ₹25,000 at 10% for 3 years, 133.1 × 250 = ₹33,275.
| Rate | 1 yr | 2 yr | 3 yr | 4 yr | 5 yr | 10 yr |
|---|---|---|---|---|---|---|
| 5% | ₹105 | ₹110.25 | ₹115.76 | ₹121.55 | ₹127.63 | ₹162.89 |
| 6% | ₹106 | ₹112.36 | ₹119.10 | ₹126.25 | ₹133.82 | ₹179.08 |
| 8% | ₹108 | ₹116.64 | ₹125.97 | ₹136.05 | ₹146.93 | ₹215.89 |
| 10% | ₹110 | ₹121 | ₹133.10 | ₹146.41 | ₹161.05 | ₹259.37 |
| 12% | ₹112 | ₹125.44 | ₹140.49 | ₹157.35 | ₹176.23 | ₹310.58 |
| 15% | ₹115 | ₹132.25 | ₹152.09 | ₹174.90 | ₹201.14 | ₹404.56 |
| 18% | ₹118 | ₹139.24 | ₹164.30 | ₹193.88 | ₹228.78 | ₹523.38 |
| 20% | ₹120 | ₹144 | ₹172.80 | ₹207.36 | ₹248.83 | ₹619.17 |
Practice questions with answers
- Find the compound interest on ₹15,000 at 10% a year for 2 years, added yearly. Answer: A = ₹18,150, CI = ₹3,150.
- Find the amount on ₹40,000 at 8% a year for 1 year, added half-yearly. Answer: 40,000 × 1.04² = ₹43,264.
- Find the compound interest on ₹25,000 at 12% a year for 1 year, added quarterly. Answer: 25,000 × 1.03⁴ = ₹28,137.72, so CI = ₹3,137.72.
- At what yearly rate does ₹6,250 become ₹7,290 in 2 years, added yearly? Answer: √(7,290 ÷ 6,250) = 1.08, so 8%.
- In how many years does ₹2,000 become ₹2,662 at 10% a year? Answer: 1.331 = 1.1^3, so 3 years.
Check any of these in the compound interest calculator, which shows the formula with your numbers and every rest. It rounds each rest to the paisa, as a ledger does, so it can show a paisa more or less than the textbook answer. For how compound interest compares with simple interest, and the CI − SI shortcuts, read simple vs compound interest.
6 short answersCompound interest formula: quick answers
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What is the formula for the amount (mishradhan) in compound interest?
Amount A = P × (1 + R ÷ 100)^n, where P is the principal, R the yearly rate in % and n the years; the compound interest is A − P. ₹5,000 at 6% for 3 years: 5,000 × 1.06³ = ₹5,955.08, so the interest is ₹955.08.
How do you find compound interest when the time is in a fraction, like 2½ years?
Compound the whole years, then add simple interest on the new amount for the part year. ₹10,000 at 10% for 2½ years: 2 years give ₹12,100; half a year at 10% adds 5%, so 12,100 × 1.05 = ₹12,705. This is the usual exam method and how our calculator works.
How do you find the rate in compound interest?
Divide the amount by the principal, take the n-th root, subtract 1 and multiply by 100: R = 100 × [(A ÷ P)^(1/n) − 1]. ₹10,000 that became ₹11,910.16 in 3 years: 1.191016^(1/3) = 1.06, so the rate is 6% a year.
How do you find the time in compound interest without logs?
Multiply the principal by (1 + R ÷ 100) one year at a time until you reach the amount; the number of steps is the years. ₹5,000 at 10% grows to ₹5,500, then ₹6,050, then ₹6,655, so it becomes ₹6,655 in 3 years. With logs: n = log(A ÷ P) ÷ log(1 + R ÷ 100).
How do you find the principal when the compound interest is given?
Divide the interest by [(1 + R ÷ 100)^n − 1]. If the compound interest for 2 years at 5% is ₹1,025: (1.05)² − 1 = 0.1025, so P = 1,025 ÷ 0.1025 = ₹10,000.
What is the formula when the rate is different each year?
Multiply by a separate bracket for each year: A = P × (1 + R₁ ÷ 100) × (1 + R₂ ÷ 100) and so on. ₹50,000 at 10% in the first year and 12% in the second: 50,000 × 1.1 × 1.12 = ₹61,600, so the interest is ₹11,600.