Master the Golden Ratio Method - Solve CI Problems Without Power Formulas in Seconds! Trusted by 50,000+ IBPS, SBI, SSC aspirants!
Interest is the cost of borrowing money or the reward for saving it. Whether you're taking a loan or making a fixed deposit, understanding Simple Interest (SI) and Compound Interest (CI) is crucial � both in real life and competitive exams!
Linear Growth
Interest on Principal only
Grows in a straight line
Exponential Growth
Interest on Interest
Grows like a curve
In IBPS PO 2023, 3-5 questions came directly from SI/CI. The Golden Ratio Method helped toppers solve CI for 3 years in under 20 seconds � while others struggled with power calculations. That's 5+ minutes saved for the Quant section!
Simple Interest is calculated only on the principal amount. The interest remains the same every year.
Where: P = Principal (Initial Amount), R = Rate of Interest (% per annum), T = Time (in years)
Question: Calculate SI on ?10,000 at 5% for 3 years.
Solution:
� SI = (P � R � T) / 100
� SI = (10,000 � 5 � 3) / 100
� SI = 1,50,000 / 100 = ?1,500
? Total Amount = 10,000 + 1,500 = ?11,500
Compound Interest is calculated on principal + accumulated interest. It grows exponentially!
Where: A = Final Amount, P = Principal, R = Rate, n = Number of years
Question: Calculate CI on ?10,000 at 5% compounded annually for 3 years.
Solution:
� A = P � (1 + R/100)n
� A = 10,000 � (1.05)�
� A = 10,000 � 1.157625 = ?11,576.25
� CI = 11,576.25 - 10,000 = ?1,576.25
? Notice: CI (?1,576) > SI (?1,500) for the same period!
Calculating (1.05)� or (1.10)4 in exams is time-consuming. Use the Golden Ratio Method to solve CI problems without any power calculations!
| Years | Ratio | How to Use |
|---|---|---|
| 2 Years | 2 : 1 | 2�(First Year Interest) + 1�(Interest on Interest) |
| 3 Years | 3 : 3 : 1 | 3�I1 + 3�I2 + 1�I3 |
| 4 Years | 4 : 6 : 4 : 1 | 4�I1 + 6�I2 + 4�I3 + 1�I4 |
I1 = R% of Principal. For ?10,000 at 10%, I1 = ?1,000
I2 = R% of I1, I3 = R% of I2, and so on. Each level is 10% of previous for 10% rate.
Multiply each interest level with corresponding ratio number and sum up!
No power calculations needed � pure mental math!
Question: Find CI on ?10,000 at 10% for 3 years.
Solution using Golden Ratio (3:3:1):
� I1 = 10% of 10,000 = ?1,000
� I2 = 10% of 1,000 = ?100
� I3 = 10% of 100 = ?10
� Apply Ratio: (3�1000) + (3�100) + (1�10)
� CI = 3000 + 300 + 10 = ?3,310
? Verify: Using formula: 10,000 � (1.1)� = 13,310 ? CI = ?3,310 ?
For 10% rate, memorize these multipliers:
� (1.1)� = 1.21 ? Amount becomes 1.21� Principal
� (1.1)� = 1.331 ? Amount becomes 1.331� Principal
� (1.1)4 = 1.4641
For 20%: (1.2)� = 1.44, (1.2)� = 1.728
When questions ask for the difference between CI and SI, use these direct formulas:
Question: Find the difference between CI and SI for ?5,000 at 10% for 2 years.
Solution:
� Difference = P � (R/100)�
� Difference = 5,000 � (10/100)�
� Difference = 5,000 � 0.01 = ?50
? Quick Check: SI = 1,000, CI = (5,000 � 1.21) - 5,000 = 1,050 ? Diff = ?50 ?
For 2 years, CI - SI difference is simply:
Difference = SI for 1 year � (R/100)
Example: SI for 1 year = ?500, Rate = 10%
Difference = 500 � 0.1 = ?50
Interest can be compounded at different intervals. The more frequent the compounding, the higher the final amount!
n = 1
Once per year
n = 2
R/2, 2T
n = 4
R/4, 4T
n = 12
R/12, 12T
Question: Find CI on ?1,000 at 10% compounded half-yearly for 1 year.
Solution:
� Half-yearly: R = 10/2 = 5%, n = 2 times
� A = 1,000 � (1.05)�
� A = 1,000 � 1.1025 = ?1,102.50
� CI = ?102.50
? Compare: Annual CI = ?100, Half-yearly CI = ?102.50 (More!)
For quick calculations, memorize:
� (1.05)� = 1.1025, (1.05)� = 1.157625
� (1.1)� = 1.21, (1.1)� = 1.331
� (1.2)� = 1.44, (1.2)� = 1.728
10% = �10, 5% = �20, 25% = �4
Calculate first-year interest mentally using division!
For 1 year only, CI and SI are always equal! Use this to eliminate wrong options quickly.
To find how many years for money to double: Years � 72 / Rate
At 12%: 72/12 = 6 years to double your money!
Set a 45-second timer per question. Use Golden Ratio for 2-3 year problems, formulas for 1 year problems.
SI = (P � R � T) / 100
A = P(1 + R/100)n
Diff = P � (R/100)�
Doubling Time � 72/R
Ab aapko SI & CI ki poori samajh aa gayi! Time to test your skills with real exam-level questions!
Start Practice Now ?