Before you begin
What you need: Percentages, powers and simple interest.
- Explain interest on accumulated interest
- Calculate amount and compound interest
- Adjust the rate and period count for compounding frequency
Understand the idea
Each period begins with a new balance
Compound interest is applied to the current balance. At 10%, ₹1,000 becomes ₹1,100 after one year; the next year's interest is ₹110, not ₹100.
Multiply the growth factors
Each full period multiplies the balance by 1 + i, where i is the period rate as a decimal. Repeating this n times gives P(1 + i)ⁿ.
Frequency changes both inputs
For a nominal annual rate compounded half-yearly, divide the annual percentage rate by 2 and use twice as many periods. This is different from an effective annual rate. Follow the question's convention.
Watch the increments grow
A method you can reuse
A = P(1 + r/100)ⁿ; CI = A − P
Here r is the percentage rate per compounding period and n is the number of full periods.- Determine the rate per period and number of periods.
- Multiply principal by the growth factor raised to that period count.
- Subtract the original principal for interest; round money at the end.
For two years at the same annual rate r%, CI − SI = P(r/100)², with annual compounding.
Worked examples
Read the question first. Try a step yourself, then compare your reasoning.
Annual compounding
Find CI on ₹5,000 at 10% for two years, compounded annually.
- Growth factor = 1.1.
- A = 5000 × 1.1² = ₹6050.
- CI = 6050 − 5000.
Half-yearly compounding
₹10,000 earns a nominal 10% annual rate compounded half-yearly for one year. Find CI.
- Rate per half-year = 5%; periods = 2.
- A = 10000 × 1.05² = ₹11025.
- CI = 11025 − 10000.
Compare with simple interest
Compare SI and CI on ₹1,000 at 10% for two years with annual compounding.
- SI = 1000 × 10 × 2/100 = ₹200.
- CI = 1000 × 1.1² − 1000 = ₹210.
- The extra ₹10 is interest on the first year's ₹100 interest.
Check your understanding
Quick questions, with explanations. These are for self-study and do not affect your account score.
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