How to Solve Simple and Compound Interest Problems
Solve simple and compound interest aptitude problems with formulas, the two-year shortcut, a worked example and practice questions with answers.
Expected Interview Answer
Simple interest grows linearly on the original principal (SI = P×R×T/100), while compound interest grows on principal plus accumulated interest, giving CI = P×(1+R/100)^T − P.
With simple interest, the interest earned each period is identical because it is always computed on the fixed original principal. With compound interest, each period’s interest is computed on the previous period’s new balance, so the interest itself earns interest, producing exponential rather than linear growth. For short periods and small rates the two are close, but the gap widens with time. A common shortcut for two years: CI − SI = P×(R/100)^2, useful for quickly finding one unknown when the other is known.
- One pair of formulas covers most bank/loan problems
- The CI − SI shortcut solves two-year problems fast
- Clarifies why compounding accelerates growth over time
AI Mentor Explanation
A batter who scores a fixed 40 runs every match (simple interest) accumulates linearly: 40 per game, always the same increment. A batter whose scoring rate compounds — this match’s form boosts next match’s runs — grows faster and faster, the way a compounding score snowballs beyond simple linear addition. Formally, SI = P×R×T/100 adds a constant amount each period, while CI = P×(1+R/100)^T − P lets each period’s gain build on the last, producing the accelerating curve.
Worked example
Simple Interest
- SI = 10000×10×2/100
- = 2000
Compound Interest
- CI = 10000×1.1² − 10000
- = 2100
Difference (2 yrs)
- CI − SI = P(R/100)²
- = 100
Step-by-Step Explanation
Step 1
Simple interest formula
SI = P × R × T / 100 — always on the original principal.
Step 2
Compound interest formula
CI = P × (1 + R/100)^T − P — compounds on the growing balance.
Step 3
Two-year shortcut
For T = 2, CI − SI = P × (R/100)^2.
Step 4
Compare growth
CI equals SI in year one, then always exceeds it as T grows.
What Interviewer Expects
- Correct SI and CI formulas
- Understanding why CI compounds on a growing base
- The CI − SI = P(R/100)^2 shortcut for 2 years
- Recognition that CI = SI only in the first year
Common Mistakes
- Applying the CI formula but computing interest on the original principal only
- Forgetting that rate and time must match the compounding period
- Misremembering the two-year CI − SI shortcut
- Confusing annual compounding with half-yearly/quarterly rates
Best Answer (HR Friendly)
“Simple interest is a flat amount every period, computed on the original principal — P times R times T over 100. Compound interest recalculates on the growing balance each period, so it earns interest on interest. That is why compound interest always overtakes simple interest after the first year, and the gap widens the longer the money sits.”
Follow-up Questions
- How does the compounding frequency (yearly vs quarterly) change the CI formula?
- How do you find the principal given the compound interest and rate?
- What is the effective annual rate when interest compounds quarterly?
- How would you derive the CI − SI shortcut for 3 years?
MCQ Practice
1. Principal = 5000, Rate = 8% per annum, Time = 3 years. Simple interest is?
SI = 5000 × 8 × 3 / 100 = 1200.
2. Principal = 2000, Rate = 10% per annum compounded annually, Time = 2 years. Compound interest is?
CI = 2000×(1.1)² − 2000 = 2420 − 2000 = 420.
3. For the same P, R and T (T ≥ 2), how do SI and CI compare?
CI compounds on a growing balance, so it matches SI at T=1 and exceeds it thereafter.
Flash Cards
Simple interest formula? — SI = P × R × T / 100, always on original principal.
Compound interest formula? — CI = P × (1 + R/100)^T − P.
Two-year CI − SI shortcut? — CI − SI = P × (R/100)².
When are CI and SI equal? — Only in the first compounding period (T = 1).