Interest is calculated from a principal, a rate and a period of time. Simple interest uses the original principal throughout. Compound interest adds interest to the balance at each compounding step, so later interest is calculated on a changing amount. These notes use original school-level examples, not financial advice.
Simple interest
When P is the principal, r is the annual percentage rate and t is time in years, simple interest SI = Prt/100. The total amount is A = P + SI. Convert months into years when the rate is annual: six months means t = 1/2.
The units of rate and time must match. A monthly rate cannot be combined with a time measured in years without a suitable conversion.
- Principal is the starting amount.
- Amount includes principal and interest; interest alone does not.
Annual compound interest
With annual compounding at a constant annual rate r%, A = P(1 + r/100)ⁿ after n complete years. Compound interest is A − P. For two years, you can also calculate the first year’s amount and use it as the second year’s principal.
Half-yearly compounding uses a different period and rate per period. Do not use the annual formula unchanged when the question specifies another compounding frequency. For changing annual rates, multiply by each year’s growth factor separately.
Put it into practice
A worked example
Find compound interest on ₹5,000 at 10% per year for two years, compounded annually.
- First year: ₹5,000 × 1.10 = ₹5,500.
- Second year: ₹5,500 × 1.10 = ₹6,050.
- Subtract the original principal: ₹6,050 − ₹5,000.
Answer: Compound interest is ₹1,050. The final amount is ₹6,050.
Try it yourself
Have a go before revealing the answer.
Find simple interest on ₹3,000 at 8% per year for six months.
Show answer
SI = 3000 × 8 × 0.5 / 100 = ₹120.
Answer: SI = 3000 × 8 × 0.5 / 100 = ₹120.
For the worked example, how much greater is CI than SI over two years?
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SI = ₹1,000, so CI exceeds it by ₹50.
Answer: SI = ₹1,000, so CI exceeds it by ₹50.
Watch out for these
- Do not report the final amount when asked only for interest.
- Check whether the period is in months or years and how often compounding happens.
Continue with official resources
Match these concept notes to your current textbook and syllabus. They are independent explanations, not official board publications.