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Quantitative Aptitude›Ch 2: Commercial Maths›Compound Interest Masterclass
Master annual, half-yearly compounding and CI-SI differences for exams
Compound Interest (CI) means interest is added to the principal each period, so interest also earns interest. The total amount is calculated using the formula Amount = Principal times one plus rate upon hundred raised to the power time.
Quick Memory Hooks
| Time Period | Formula for CI minus SI | Key Application |
|---|---|---|
| 2 Years | P * (R/100)^2 | Direct diff questions |
| 3 Years | P * (R/100)^2 * (300+R)/100 | Longer tenure sums |
| Ratio Method (2 yr) | CI : SI = (200+R) : 200 | Fast ratio queries |
Annual
(Once a year)
Once a year
Interest compounded yearly uses standard R and T.
Half-Yearly
(Twice a year)
Twice a year
Rate becomes half and time becomes double.
Quarterly
(Four times a year)
Four times a year
Rate becomes one-fourth and time becomes four times.
CI vs SI
(Interest gap)
Interest gap
CI is always greater than SI for more than 1 year.
Forgetting to halve rate in half-yearlyAlways use R/2 for half-yearly compounding
Students apply full rate even when compounding is half-yearly, leading to wrong amounts.
Using SI formula for CI questionsUse Successive percentage or Amount formula
CI grows exponentially, simple interest formula does not apply directly.
Confusing 2-year and 3-year diff formulaRemember extra factor (300+R)/100 for 3 years
Applying the 2-year difference formula for 3-year questions is a frequent exam blunder.
Q1.Find the difference between CI and SI on Rs. 10,000 for 2 years at 10% per annum compounded annually.
Q2.What is the compound interest on Rs. 8,000 for 1.5 years at 20% per annum compounded half-yearly?