Aptitude · Lesson 7 of 9
Simple & compound interest
SI and CI formulas, compounding periods and the CI − SI shortcut.
- Simple interest:
SI = P × R × T / 100; amount = P + SI. - Compound interest:
A = P (1 + R/100)ᵀ; CI = A − P. - Half-yearly compounding: use R/2 and 2T; quarterly: R/4 and 4T.
- For 2 years,
CI − SI = P (R/100)². - Money doubles under SI in
100 / Ryears; under CI roughly72 / Ryears (rule of 72).
Example: Find the simple interest on ₹25,000 at 8% per year for 3 years.
- SI = 25,000 × 8 × 3 / 100.
Answer: ₹6,000
Example: Find the compound interest on ₹10,000 at 10% per year for 2 years.
- A = 10,000 × 1.1 × 1.1 = 12,100.
- CI = 12,100 − 10,000.
Answer: ₹2,100 (SI would be ₹2,000; difference = 10,000 × 0.01 = ₹100)
Key points
- SI grows linearly; CI grows on the growing amount.
- Adjust rate and periods for half-yearly/quarterly.
- 2-year CI − SI = P(R/100)².
Quick check
At what SI rate does money double in 8 years?
Interest = principal in 8 years → R = 100/8 = 12.5%.
Practice task
The difference between CI and SI on a sum for 2 years at 5% is ₹50. Find the sum.
Show answer
P × (5/100)² = 50 → P × 0.0025 = 50 → P = ₹20,000.
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Why do banks quote an effective annual rate?
With more frequent compounding the actual yearly growth exceeds the nominal rate; the effective rate makes products comparable.
Roughly how long to double money at 6% compound?
Rule of 72: 72 / 6 ≈ 12 years.
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