⚡ Simple Interest - Formulas & Shortcuts

Quick reference guide for all Simple Interest formulas and time-saving shortcuts.

📐 Core Formulas

1. Basic Formula

SI = (P × R × T) / 100

Remember: P-R-T over 100

2. Amount Formula

A = P + SI

OR

A = P[1 + (RT/100)]

3. Finding Principal

P = (SI × 100) / (R × T)

OR

P = (A × 100) / (100 + RT)

4. Finding Rate

R = (SI × 100) / (P × T)

5. Finding Time

T = (SI × 100) / (P × R)

⚡ Quick Shortcuts

Shortcut 1: When SI = Principal

If SI = P, then:
RT = 100

Example: If R = 5%, then T = 20 years
         If T = 10 years, then R = 10%

Shortcut 2: When Amount = 2 × Principal

If A = 2P, then SI = P
Therefore: RT = 100

Shortcut 3: When Amount = 3 × Principal

If A = 3P, then SI = 2P
Therefore: RT = 200

General Formula:

If A = nP, then:
RT = 100(n - 1)

Shortcut 4: Mental Calculation for R = 10%

For R = 10% and T = 1 year:
SI = P/10

For R = 10% and T = 2 years:
SI = P/5

For R = 10% and T = n years:
SI = nP/10

Shortcut 5: For R = 5%

For R = 5% and T = 2 years:
SI = P/10

For R = 5% and T = 4 years:
SI = P/5

For R = 5% and T = 20 years:
SI = P (doubles!)

Shortcut 6: Ratio Method

If same principal at different rates/times:
SI₁ : SI₂ = (R₁ × T₁) : (R₂ × T₂)

Example:

P = ₹10,000 in both cases
Case A: 6% for 2 years
Case B: 4% for 3 years

SI ratio = (6×2):(4×3) = 12:12 = 1:1
So both give same SI = ₹1,200

🎯 Pattern-Based Shortcuts

Pattern 1: Doubling Time

Time to double = 100/R years

Example:
At 5% p.a., time to double = 100/5 = 20 years
At 10% p.a., time to double = 100/10 = 10 years
At 20% p.a., time to double = 100/20 = 5 years

Pattern 2: Tripling Time

Time to triple = 200/R years

Example:
At 10% p.a., time to triple = 200/10 = 20 years
At 5% p.a., time to triple = 200/5 = 40 years

Pattern 3: n-times Multiplier

Time for A = nP is:
T = 100(n-1)/R years

📊 Time Conversion Shortcuts

Months to Years

1 month = 1/12 year
2 months = 1/6 year
3 months = 1/4 year
4 months = 1/3 year
6 months = 1/2 year
8 months = 2/3 year
9 months = 3/4 year

Quick Trick:

For SI calculation with months:
SI = (P × R × Months) / 1200

Days to Years

Common conversions:
30 days = 1/12 year
60 days = 1/6 year
73 days = 1/5 year
90 days = 1/4 year
120 days = 1/3 year
180 days = 1/2 year

Quick Trick:

For SI calculation with days:
SI = (P × R × Days) / 36500

🔢 Percentage-Based Formulas

When SI is given as % of Principal

If SI = x% of P for n years:
R = (x × 100)/(100 × n) = x/n %

Example:
If SI = 40% of P in 5 years:
R = 40/5 = 8% p.a.

When Amount is given as % more than Principal

If A = (100 + x)% of P:
SI = x% of P
RT = x

Example:
If A = 125% of P:
SI = 25% of P
RT = 25

⚡ Super Quick Calculations

For R = 12% (Common in Banking)

For T = 1 year: SI = 12P/100 = 3P/25
For T = 2 years: SI = 24P/100 = 6P/25
For T = 5 years: SI = 60P/100 = 3P/5

For R = 8%

For T = 1 year: SI = 8P/100 = 2P/25
For T = 5 years: SI = 40P/100 = 2P/5
For T = 12.5 years: SI = P (doubles!)

💡 Exam-Specific Shortcuts

Shortcut A: Two Different Investments

If P₁ at R₁% for T₁ years and P₂ at R₂% for T₂ years give same SI:

P₁(R₁ × T₁) = P₂(R₂ × T₂)

Shortcut B: Total SI from Multiple Investments

Total SI = SI₁ + SI₂ + SI₃ + ...
         = (P₁R₁T₁ + P₂R₂T₂ + P₃R₃T₃)/100

Shortcut C: Average Rate

If same principal at two different rates R₁% and R₂%:
Average SI per year = P(R₁ + R₂)/200

📋 Formula Summary Table

🎯 Shortcut Application Examples

Example 1: Using Doubling Formula

Q: At what rate will a sum double in 8 years?

Shortcut Method:

Time to double = 100/R
8 = 100/R
R = 100/8 = 12.5% p.a.

Time Saved: 30 seconds vs traditional method!

Example 2: Using Ratio Method

Q: ₹10,000 at 6% for 3 years vs 9% for 2 years. Which gives more SI?

Shortcut Method:

SI ratio = (R₁T₁):(R₂T₂)
        = (6×3):(9×2)
        = 18:18
        = 1:1 (Equal!)

No calculation needed!

Example 3: Using Amount Formula

Q: ₹5,000 becomes ₹6,000 in 4 years. Find rate.

Shortcut Method:

A = P[1 + RT/100]
6000 = 5000[1 + R×4/100]
6/5 = 1 + 4R/100
1/5 = 4R/100
R = 100/(5×4) = 5% p.a.

🚀 Speed Practice Tips

1. Memorize these:

   • 100/R = Time to double
   • 200/R = Time to triple
   • RT = 100 when SI = P

2. Use ratio method when comparing two scenarios

3. Convert months quickly:

   • Divide by 12 for rough calculation
   • Use 1200 in denominator for exact SI

4. Pattern recognition:

   • If R and T are multiples of each other = easy calculation
   • Example: R=5%, T=4 years → RT=20 → SI=P/5

📚 Related Resources

• Simple Interest Theory
• Practice Questions
• All Formulas Sheet
• Compound Interest Formulas

Pro Tip: Practice these shortcuts on 100+ questions to achieve <30 second solving time! ⚡