Compound interest meaning
Compound interest is interest calculated on the original amount and on all the interest added to it so far. Each period's interest becomes part of the balance, so the next period's interest is larger. In Hindi it is called चक्रवृद्धि ब्याज (chakravriddhi byaj).
Bank FDs and RDs, PPF and loans in India all compound; only a few loans and textbook sums use simple interest. Work out any amount in the Compound Interest Calculator.
Compound interest formula
The compound interest formula is:
A = P × (1 + r ÷ n)^(n × t), and CI = A − P
- A = final amount
- P = principal (the amount you start with)
- r = annual interest rate as a decimal (8% = 0.08)
- n = number of times interest is compounded in a year
- t = time in years
When interest is compounded once a year, this simplifies to A = P × (1 + R ÷ 100)^t, where R is the rate in percent.
Compound interest formula with example
₹1,00,000 at 8% a year, compounded yearly, for 3 years:
- A = 1,00,000 × (1.08)^3
- (1.08)^3 = 1.259712
- A = ₹1,25,971.20
- CI = 1,25,971.20 − 1,00,000 = ₹25,971.20
Year by year, the interest is ₹8,000, then ₹8,640, then ₹9,331.20: each year's interest is larger because it is charged on a larger balance.
Compound interest compounded quarterly
When interest is compounded quarterly, it is added 4 times a year, so n = 4: use r ÷ 4 for the rate per quarter and 4 × t for the number of quarters. The more often interest is compounded, the more you earn.
₹1,00,000 at 8% for 3 years:
| Compounding | Formula | Amount | Interest |
|---|---|---|---|
| Yearly | 1,00,000 × 1.08^3 | ₹1,25,971 | ₹25,971 |
| Half-yearly | 1,00,000 × 1.04^6 | ₹1,26,532 | ₹26,532 |
| Quarterly | 1,00,000 × 1.02^12 | ₹1,26,824 | ₹26,824 |
| Monthly | 1,00,000 × (1 + 0.08/12)^36 | ₹1,27,024 | ₹27,024 |
Most Indian bank FDs and RDs compound quarterly; PPF compounds yearly. Compare deposits in the FD Calculator.
Compound interest formula for half yearly
For half-yearly compounding, interest is added twice a year: A = P × (1 + R ÷ 200)^(2t), with R in percent. For ₹1,00,000 at 8% for 3 years, that is 1,00,000 × (1.04)^6 = ₹1,26,532, of which ₹26,532 is interest.
Difference between simple interest and compound interest
Simple interest is charged only on the original principal; compound interest is charged on the principal plus the interest already added. Over time, compound interest grows much faster.
| Simple interest | Compound interest | |
|---|---|---|
| Charged on | Principal only | Principal + past interest |
| Formula | SI = P × R × T ÷ 100 | A = P × (1 + R ÷ 100)^T |
| ₹1 lakh at 8% for 3 years | ₹24,000 | ₹25,971 |
| Growth | Same amount each year | Larger amount each year |
Work out simple interest in the Simple Interest Calculator.
Difference between simple interest and compound interest for 2 years formula
For yearly compounding, the difference between compound and simple interest is:
- 2 yearsCI − SI = P × (R ÷ 100)^2
- 3 yearsCI − SI = P × (R ÷ 100)^2 × (3 + R ÷ 100)
For ₹1,00,000 at 8%: the difference is ₹640 over 2 years and ₹1,971.20 over 3 years. These shortcuts are common in bank, SSC and other competitive exams.
Rule of 72
The Rule of 72 says that money doubles in about 72 ÷ interest rate years with compound interest. At 8% it doubles in about 9 years; at 12%, about 6.
| Rate | Doubles (72 ÷ rate) | Exact | Triples (114 ÷ rate) |
|---|---|---|---|
| 6% | 12 years | 11.9 years | 19 years |
| 8% | 9 years | 9.0 years | 14.3 years |
| 12% | 6 years | 6.1 years | 9.5 years |
The Rule of 114 estimates when money triples and the Rule of 144 when it quadruples. They are close for rates between about 6% and 12%.
Compound interest formula in Excel
In Excel or Google Sheets, compound interest can be calculated with =P*(1+r/n)^(n*t) or with the FV function: =FV(rate/n, n*t, 0, -P).
For ₹1,00,000 at 8% compounded quarterly for 3 years, =FV(8%/4, 12, 0, -100000) returns ₹1,26,824. Subtract the principal to get the interest.
