Quantitative Aptitude Fundamentals

Interest calculations test whether you understand exponential growth. Companies analyze investment returns, loan calculations, and financial projections using these concepts. For a management trainee role, understanding interest calculations could mean the difference between securing millions in loans or losing company money.

Simple Interest – The Linear Growth Model

Simple Interest assumes that interest is calculated only on the principal amount, not on accumulated interest.

Formula:
SI=P×R×T100\text{SI} = \frac{P \times R \times T}{100}SI=100P×R×T

Where:

• P = Principal (initial amount borrowed/invested)
  
• R = Rate of interest (per annum, in %)
  
• T = Time (in years)
  

Amount after Simple Interest:
A=P+SI=P+P×R×T100=P(1+R×T100)A = P + \text{SI} = P + \frac{P \times R \times T}{100} = P \left(1 + \frac{R \times T}{100}\right)A=P+SI=P+100P×R×T=P(1+100R×T)

Practical Example: Bank Savings

You deposit ₹10,000 in a bank account that offers 5% simple interest per annum. How much money do you have after 3 years?

Solution:
SI=10,000×5×3100=150,000100=₹1,500\text{SI} = \frac{10,000 \times 5 \times 3}{100} = \frac{150,000}{100} = ₹1,500SI=10010,000×5×3=100150,000=₹1,500

Total Amount = ₹10,000 + ₹1,500 = ₹11,500

Understanding the Timeline:

• Year 1: Interest earned = ₹500 (5% of ₹10,000)
  
• Year 2: Interest earned = ₹500 (5% of ₹10,000, not on the new total)
  
• Year 3: Interest earned = ₹500 (5% of ₹10,000)
  

Notice how the interest remains constant each year? That’s simple interest—it doesn’t compound.

Compound Interest – The Exponential Growth Model

Compound Interest is where interest is calculated on the principal plus the accumulated interest from previous periods.

Formula:
A=P(1+R100)TA = P \left(1 + \frac{R}{100}\right)^TA=P(1+100R)T

Where A is the final amount after T years.

Compound Interest Amount:
CI=A−P=P[(1+R100)T−1]\text{CI} = A – P = P \left[\left(1 + \frac{R}{100}\right)^T – 1\right]CI=A−P=P[(1+100R)T−1]

Same Example with Compound Interest:

₹10,000 invested at 5% compound interest per annum for 3 years.

A=10,000(1+5100)3=10,000×(1.05)3A = 10,000 \left(1 + \frac{5}{100}\right)^3 = 10,000 \times (1.05)^3A=10,000(1+1005)3=10,000×(1.05)3

A=10,000×1.157625=₹11,576.25A = 10,000 \times 1.157625 = ₹11,576.25A=10,000×1.157625=₹11,576.25

Compound Interest = ₹11,576.25 – ₹10,000 = ₹1,576.25

The Key Difference:

• Simple Interest: ₹1,500
  
• Compound Interest: ₹1,576.25
  
• Difference: ₹76.25 (extra earnings because interest earns interest)
  

This might seem small, but over longer periods, the difference becomes massive. This is why Warren Buffett emphasizes compound interest as “the eighth wonder of the world.”

Critical Placement Test Variation: Half-Yearly and Quarterly Compounding

Most students memorize the annual compounding formula and miss questions about half-yearly or quarterly compounding.

If interest compounds semi-annually (twice per year):
A=P(1+R200)2TA = P \left(1 + \frac{R}{200}\right)^{2T}A=P(1+200R)2T

Notice: R is divided by 200 (not 100), and T is multiplied by 2.

Why? When compounding happens twice a year, the annual rate R is split into two parts (R/2 each), and the number of compounding periods doubles.

Example: ₹5,000 at 10% per annum, compounded half-yearly, for 2 years.

A=5,000(1+10200)4=5,000×(1.05)4A = 5,000 \left(1 + \frac{10}{200}\right)^{4} = 5,000 \times (1.05)^4A=5,000(1+20010)4=5,000×(1.05)4

A=5,000×1.21550625=₹6,077.53A = 5,000 \times 1.21550625 = ₹6,077.53A=5,000×1.21550625=₹6,077.53

Common Student Mistakes to Avoid:

1. Using simple interest formula for compound interest – Always check the problem statement
   
2. Forgetting to adjust R and T for compounding frequency – If quarterly, use R/400 and 4T
   
3. Calculating total amount instead of just the interest – Some questions ask for SI/CI amount alone, not the total