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 ā 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 ā 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 ā¹10,000 at 5% for 3 years.
Solution:
ā¢ SI = (P Ć R Ć T) / 100
ā¢ SI = (10,000 Ć 5 Ć 3) / 100
ā¢ SI = 1,50,000 / 100 = ā¹1,500
ā
Total Amount = 10,000 + 1,500 = ā¹11,500
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 ā¹10,000 at 5% compounded annually for 3 years.
Solution:
ā¢ A = P Ć (1 + R/100)āæ
ā¢ A = 10,000 Ć (1.05)Ā³
ā¢ A = 10,000 Ć 1.157625 = ā¹11,576.25
ā¢ CI = 11,576.25 - 10,000 = ā¹1,576.25
ā
Notice: CI (ā¹1,576) > SI (ā¹1,500) for the same period!
Calculating (1.05)Ā³ or (1.10)ā“ 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 | 2Ć(First Year Interest) + 1Ć(Interest on Interest) |
| 3 Years | 3 : 3 : 1 | 3ĆIā + 3ĆIā + 1ĆIā |
| 4 Years | 4 : 6 : 4 : 1 | 4ĆIā + 6ĆIā + 4ĆIā + 1ĆIā |
Iā = R% of Principal. For ā¹10,000 at 10%, Iā = ā¹1,000
Iā = R% of Iā, Iā = R% of Iā, 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 ā pure mental math!
Question: Find CI on ā¹10,000 at 10% for 3 years.
Solution using Golden Ratio (3:3:1):
ā¢ Iā = 10% of 10,000 = ā¹1,000
ā¢ Iā = 10% of 1,000 = ā¹100
ā¢ Iā = 10% of 100 = ā¹10
ā¢ Apply Ratio: (3Ć1000) + (3Ć100) + (1Ć10)
ā¢ CI = 3000 + 300 + 10 = ā¹3,310
ā
Verify: Using formula: 10,000 Ć (1.1)Ā³ = 13,310 ā CI = ā¹3,310 ā
For 10% rate, memorize these multipliers:
ā¢ (1.1)Ā² = 1.21 ā Amount becomes 1.21Ć Principal
ā¢ (1.1)Ā³ = 1.331 ā Amount becomes 1.331Ć Principal
ā¢ (1.1)ā“ = 1.4641
For 20%: (1.2)Ā² = 1.44, (1.2)Ā³ = 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 ā¹5,000 at 10% for 2 years.
Solution:
ā¢ Difference = P Ć (R/100)Ā²
ā¢ Difference = 5,000 Ć (10/100)Ā²
ā¢ Difference = 5,000 Ć 0.01 = ā¹50
ā
Quick Check: SI = 1,000, CI = (5,000 Ć 1.21) - 5,000 = 1,050 ā Diff = ā¹50 ā
For 2 years, CI - SI difference is simply:
Difference = SI for 1 year Ć (R/100)
Example: SI for 1 year = ā¹500, Rate = 10%
Difference = 500 Ć 0.1 = ā¹50
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 ā¹1,000 at 10% compounded half-yearly for 1 year.
Solution:
ā¢ Half-yearly: R = 10/2 = 5%, n = 2 times
ā¢ A = 1,000 Ć (1.05)Ā²
ā¢ A = 1,000 Ć 1.1025 = ā¹1,102.50
ā¢ CI = ā¹102.50
ā
Compare: Annual CI = ā¹100, Half-yearly CI = ā¹102.50 (More!)
For quick calculations, memorize:
ā¢ (1.05)Ā² = 1.1025, (1.05)Ā³ = 1.157625
ā¢ (1.1)Ā² = 1.21, (1.1)Ā³ = 1.331
ā¢ (1.2)Ā² = 1.44, (1.2)Ā³ = 1.728
10% = Ć·10, 5% = Ć·20, 25% = Ć·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 ā 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 Ć R Ć T) / 100
A = P(1 + R/100)āæ
Diff = P Ć (R/100)Ā²
Doubling Time ā 72/R
Ab aapko SI & CI ki poori samajh aa gayi! Time to test your skills with real exam-level questions!
Start Practice Now ā