2.2 Compound Interest — Formula and Basic Application
Free study material · concepts, shortcuts & solved questions
Under Compound Interest, interest is added to the principal at the end of each compounding period, and from then on interest is earned on this new, larger amount. This is why CI grows faster than SI over time — it is “interest on interest.”
Basic formula (compounded annually):
A = P(1 + (R)/(100))^(T)
CI = A - P = P[(1 + (R)/(100))^(T) - 1]
Here R is the rate per compounding period and T is the number of compounding periods. When compounding is annual, T is simply the number of years. Notice the structural difference from SI: instead of multiplying P by a flat (RT/100) factor, CI raises the single-year multiplying factor (1+R/100) to the power T — this is exactly the “successive percentage change of the same percentage, applied T times” idea from your Percentage chapter, and keeping that link in mind will make every CI calculation feel like second nature rather than a new formula to memorise.
Solved Example 2.2.1: Find the CI on Rs. 15,000 at 10% p.a. for 2 years, compounded annually.
Solution: A = 15000 × (1.1)² = 15000 × 1.21 = Rs. 18,150. CI = 18150 − 15000 = Rs. 3,150.
Solved Example 2.2.2: Find the CI on Rs. 25,000 at 8% p.a. for 3 years.
Solution: A = 25000 × (1.08)³ = 25000 × 1.259712 = Rs. 31,492.80. CI = Rs. 6,492.80.
Solved Example 2.2.3: The CI on a sum for 2 years at 10% p.a. is Rs. 2,100. Find the sum.
Solution: CI = P[(1.1)² − 1] = P × 0.21. So P = 2100/0.21 = Rs. 10,000.
Solved Example 2.2.4: Find the CI on Rs. 12,500 at 12% p.a. for 3 years, compounded annually.
Solution: A = 12500 × (1.12)³ = 12500 × 1.404928 = Rs. 17,561.60. CI = 17561.60 − 12500 = Rs. 5,061.60. (Note the non-round rate here — carry at least four decimal places through (1.12)³ = 1.404928 to avoid rounding error, exactly as the Common Mistakes section warns.)
Solved Example 2.2.5: Find the CI on Rs. 10,000 at 5% p.a. for 4 years, compounded annually (an edge case beyond the usual 2–3 year range).
Solution: A = 10000 × (1.05)⁴ = 10000 × 1.21550625 = Rs. 12,155.0625. CI = Rs. 2,155.06 (approx). Since no clean 4-year shortcut formula exists (Section 2.6’s formula works only for 3 years), the full power expansion is unavoidable here — this is exactly the “4 years or more” trap flagged in the Common Mistakes section.