How to Solve: CUET Quant – Simple and Compound Interest

How to Solve: CUET Quant – Simple and Compound Interest

Introduction

"If you can calculate how much your ₹10,000 investment grows in 3 years—or how much extra you’ll pay on a loan—you’ve just unlocked 5-10 marks in CUET Quant. Let’s master it in 10 minutes."

What You Need To Know First

1. Percentage calculations – How to find 5% of 200 or increase 150 by 10%.
2. Basic algebra – Solving for an unknown variable (e.g., P in A = P(1 + r/100)).
3. Time conversions – Years, months, and days (e.g., 1.5 years = 1 year + 6 months).

Key Vocabulary

Formulas To Know

1. Simple Interest (SI)

Formula: SI = (P × r × t) / 100 - P = Principal (₹) - r = Rate of interest (% per year) - t = Time (years) MEMORISE THIS – Not always given on the exam sheet.

Amount (A): A = P + SI = P(1 + (r × t)/100)

2. Compound Interest (CI)

Formula (Annual Compounding): A = P(1 + r/100)^t - A = Amount after t years - P, r, t = Same as above MEMORISE THIS – Given on some exam sheets, but not all.

Compound Interest (CI): CI = A – P = P[(1 + r/100)^t – 1]

For different compounding periods (half-yearly, quarterly): A = P(1 + r/(100 × n))^(n × t) - n = Number of compounding periods per year (e.g., 2 for half-yearly, 4 for quarterly).

Step-by-Step Method

For Simple Interest Problems:

1. Identify the given values: P, r, t.
2. Check units: Convert t to years if given in months/days.
3. 6 months = 0.5 years
4. 3 months = 0.25 years
5. Plug into formula: SI = (P × r × t) / 100.
6. Calculate Amount (A): A = P + SI.
7. Answer the question: If asked for SI, stop at Step 3. If asked for A, use Step 4.

For Compound Interest Problems:

1. Identify P, r, t, and compounding frequency (annual, half-yearly, etc.).
2. Adjust rate and time if compounding is not annual:
3. Half-yearly: r → r/2, t → 2t
4. Quarterly: r → r/4, t → 4t
5. Plug into formula: A = P(1 + r/100)^t (or adjusted formula).
6. Calculate CI: CI = A – P.
7. Answer the question: If asked for A, stop at Step 3. If asked for CI, use Step 4.

Worked Example (Simple Interest)

Question: Find the simple interest on ₹8,000 at 6% per annum for 2 years. Also, find the amount.

Solution: 1. Given: P = ₹8,000, r = 6%, t = 2 years. 2. Units: t is already in years. 3. SI = (8000 × 6 × 2) / 100 = 96000 / 100 = ₹960. 4. Amount (A) = P + SI = 8000 + 960 = ₹8,960.

What we did and why: - Used the SI formula directly since t was in years. - Added SI to P to get the total amount.

Worked Examples

Example 1 – Basic (Simple Interest)

Question: A sum of ₹5,000 is lent at 8% simple interest for 3 years. Find the interest and amount.

Solution: 1. P = ₹5,000, r = 8%, t = 3 years. 2. SI = (5000 × 8 × 3) / 100 = 120000 / 100 = ₹1,200. 3. A = 5000 + 1200 = ₹6,200.

What we did and why: - Applied the SI formula step-by-step. - No unit conversions needed (t was in years).

Example 2 – Medium (Compound Interest, Half-Yearly)

Question: Find the amount on ₹10,000 at 12% per annum compounded half-yearly for 1.5 years.

Solution: 1. P = ₹10,000, r = 12%, t = 1.5 years, compounding = half-yearly. 2. Adjust rate and time:
- New r = 12%/2 = 6% per half-year.
- New t = 1.5 × 2 = 3 half-years. 3. A = 10000(1 + 6/100)^3 = 10000(1.06)^3. 4. Calculate (1.06)^3 = 1.191016. 5. A = 10000 × 1.191016 ≈ ₹11,910.16.

What we did and why: - Adjusted r and t for half-yearly compounding. - Used the CI formula with the new values.

Example 3 – Exam Style (Disguised Problem)

Question: A bank offers 10% interest compounded annually. If ₹x grows to ₹1,331 in 3 years, find x.

Solution: 1. Given: A = ₹1,331, r = 10%, t = 3 years, P = x. 2. Formula: A = P(1 + r/100)^t → 1331 = x(1 + 10/100)^3. 3. Simplify: 1331 = x(1.1)^3. 4. Calculate (1.1)^3 = 1.331. 5. 1331 = x × 1.331 → x = 1331 / 1.331 = ₹1,000.

What we did and why: - Recognized it’s a CI problem where P is unknown. - Solved for x by rearranging the formula.

Common Mistakes

Exam Traps

1-Minute Recap

"Alright, last-minute revision? Here’s the deal: 1. Simple Interest = (P × r × t)/100. Just multiply and divide—no exponents. 2. Compound Interest = P(1 + r/100)^t. If compounding is half-yearly, divide r by 2 and multiply t by 2. 3. Watch for traps: Time in months? Convert to years. Compounded quarterly? Adjust r and t. 4. Always check: Are they asking for SI/CI or Amount? Don’t mix them up. 5. Practice one problem now—pick a past paper question and solve it step-by-step. You’ve got this!

Final Tip for Teachers: - On camera: Write formulas large and clear. Pause after each step in examples. - For students: Have them solve a problem live (e.g., "Find CI on ₹2,000 at 5% for 2 years"). - Exam day: Remind them to underline key words ("compounded half-yearly," "find interest only").