Simple Interest Formula Cheat Sheet

Simple Interest Formula Cheat Sheet

Simple Interest (SI) is interest calculated only on the original principal throughout the entire time period.

The most important formula is:

SI = (P × R × T) / 100

where:

• P = Principal
• R = Rate of interest per annum
• T = Time in years
• SI = Simple Interest
• A = Total Amount

1. Basic Simple Interest Formula

SI = (P × R × T) / 100

Example

Principal = ₹5,000 Rate = 10% per annum Time = 2 years

SI = (5000 × 10 × 2) / 100
   = ₹1,000

2. Amount Formula

Amount means:

Amount = Principal + Interest

Therefore:

A = P + SI

Using the SI formula:

A = P + (P × R × T)/100

Or:

A = P(1 + RT/100)

Example

P = ₹5,000
SI = ₹1,000

Amount = 5,000 + 1,000
       = ₹6,000

3. Find Principal

From:

SI = PRT/100

we get:

P = (SI × 100) / (R × T)

Example

SI = ₹1,200 Rate = 10% Time = 3 years

P = (1200 × 100) / (10 × 3)
  = ₹4,000

4. Find Rate of Interest

R = (SI × 100) / (P × T)

Example

Principal = ₹8,000 SI = ₹2,400 Time = 3 years

R = (2400 × 100) / (8000 × 3)
  = 10%

Answer: 10% per annum

5. Find Time

T = (SI × 100) / (P × R)

Example

Principal = ₹5,000 Rate = 8% SI = ₹1,200

T = (1200 × 100) / (5000 × 8)
  = 3 years

6. Simple Interest for Months

The standard formula assumes time is in years.

Convert months into years:

T = Number of Months / 12

Therefore:

SI = (P × R × Months) / (100 × 12)

Or:

SI = (P × R × Months) / 1200

Example

Principal = ₹12,000 Rate = 10% per annum Time = 6 months

SI = (12000 × 10 × 6) / 1200
   = ₹600

7. Simple Interest for Days

If a question uses 365 days in a year:

T = Days / 365

Therefore:

SI = (P × R × Days) / (100 × 365)

If the question specifically assumes a 360-day year, use:

SI = (P × R × Days) / (100 × 360)

Exam Tip: Follow the year-length convention stated in the question.

8. Interest for One Year

For T = 1:

SI = PR/100

Example

₹20,000 at 8% per annum:

SI = 20000 × 8/100
   = ₹1,600

So yearly interest is ₹1,600.

9. Interest for Multiple Years

Under Simple Interest, the interest earned every year remains the same.

If yearly interest is I:

SI for T years = I × T

Example

₹10,000 at 12% per annum:

Interest per year
= 10000 × 12/100
= ₹1,200

For 5 years:

SI = 1,200 × 5
   = ₹6,000

10. Simple Interest Growth Shortcut

At R% simple interest for T years:

Interest = RT% of Principal

Therefore:

Amount = (100 + RT)% of Principal

Example

10% SI for 4 years:

Total Interest = 10 × 4
               = 40% of Principal

Therefore:

Amount = 140% of Principal

If principal = ₹5,000:

Amount = 5000 × 140/100
       = ₹7,000

11. Principal : Interest Ratio

At R% per annum for T years:

SI = PRT/100

Therefore:

P : SI = 100 : RT

Example

Rate = 10% Time = 5 years

P : SI
= 100 : 50
= 2 : 1

12. Principal : Amount Ratio

Since:

A = P(100 + RT)/100

we get:

P : A = 100 : (100 + RT)

Example

Rate = 10% Time = 4 years

P : A
= 100 : 140
= 5 : 7

13. Interest : Amount Ratio

Since:

SI = PRT/100

and:

A = P(100 + RT)/100

therefore:

SI : A = RT : (100 + RT)

Example

Rate = 20% Time = 2 years

SI : A
= 40 : 140
= 2 : 7

14. Amount Becomes x Times the Principal

Suppose the amount becomes n times the principal:

A = nP

Since:

A = P + SI

then:

SI = (n − 1)P

Using:

SI = PRT/100

we get:

RT = 100(n − 1)

Therefore:

T = 100(n − 1) / R

or:

R = 100(n − 1) / T

15. When Does Money Double?

If money doubles:

A = 2P

Therefore:

SI = P

So:

PRT/100 = P

Hence:

RT = 100

Therefore:

T = 100/R

Example

At 8% simple interest:

T = 100/8
  = 12.5 years

So the money doubles in 12.5 years.

16. When Does Money Triple?

If money triples:

A = 3P

Interest earned:

SI = 2P

Therefore:

RT = 200

Hence:

T = 200/R

Example

At 10% SI:

T = 200/10
  = 20 years

17. General n-Times Formula

If an amount becomes n times the principal under Simple Interest:

T = 100(n − 1)/R

Quick Table

18. If Money Doubles in T Years

If money doubles in T years:

R = 100/T

Example

Money doubles in 8 years.

R = 100/8
  = 12.5%

19. If Money Becomes n Times in T Years

R = 100(n − 1)/T

Example

Money becomes 4 times in 15 years.

R = 100(4−1)/15
  = 300/15
  = 20%

20. Amounts at Two Different Times

Under Simple Interest, the difference between amounts at two different times equals the interest earned during the interval.

If:

Amount after T₁ years = A₁
Amount after T₂ years = A₂

then:

A₂ − A₁

is the interest for:

T₂ − T₁ years

Therefore yearly interest is:

Yearly Interest
= (A₂ − A₁)/(T₂ − T₁)

21. Finding Principal from Two Amounts

Suppose:

Amount after T₁ years = A₁
Amount after T₂ years = A₂

First calculate yearly interest:

Yearly Interest
= (A₂ − A₁)/(T₂ − T₁)

Then:

Principal
= A₁ − (Yearly Interest × T₁)

Example

Amount after 3 years = ₹6,200 Amount after 5 years = ₹7,000

Difference:

7000 − 6200 = ₹800

This is interest for:

5 − 3 = 2 years

Yearly interest:

800/2 = ₹400

Interest for first 3 years:

400 × 3 = ₹1,200

Principal:

6200 − 1200
= ₹5,000

22. Finding Rate from Two Amounts

After finding yearly interest and principal:

R = (Yearly Interest / Principal) × 100

Using the previous example:

Yearly Interest = ₹400
Principal = ₹5,000

Therefore:

R = 400/5000 × 100
  = 8%

23. Difference in Interest Due to Rate Change

For the same principal and time, if the rate changes from R₁ to R₂:

Difference in SI
= P × (R₂ − R₁) × T / 100

Example

Principal = ₹10,000 Time = 2 years Rate changes from 8% to 10%.

Difference
= 10000 × (10−8) × 2 /100
= ₹400

24. Difference in Interest Due to Time Change

For the same principal and rate:

Difference in SI
= P × R × (T₂ − T₁)/100

Example

₹5,000 at 10% for 3 years instead of 2 years:

Extra SI
= 5000 × 10 × (3−2)/100
= ₹500

25. Difference in Interest Due to Principal Change

For the same rate and time:

Difference in SI
= (P₂ − P₁) × R × T /100

26. Ratio of Simple Interests

Since:

SI ∝ P × R × T

for two investments:

SI₁ : SI₂
= P₁R₁T₁ : P₂R₂T₂

Same Rate and Time

SI₁ : SI₂ = P₁ : P₂

Same Principal and Time

SI₁ : SI₂ = R₁ : R₂

Same Principal and Rate

SI₁ : SI₂ = T₁ : T₂

27. Split Investment at Different Rates

If total principal P is divided into two parts:

P₁ + P₂ = P

Total Simple Interest:

SI
= (P₁R₁T₁)/100
+ (P₂R₂T₂)/100

If both are invested for the same time T:

SI
= T(P₁R₁ + P₂R₂)/100

28. Average Rate Shortcut

If different amounts are invested for the same period at different rates:

Average Rate
= (P₁R₁ + P₂R₂ + ...)/(P₁ + P₂ + ...)

Example

₹4,000 at 10% ₹6,000 at 15%

Average Rate
= (4000×10 + 6000×15)/10000
= 13%

So the combined investment earns the same Simple Interest as ₹10,000 invested at 13%, provided the time period is the same.

29. Equal Amounts at Different Rates

If equal amounts are invested at rates R₁ and R₂ for the same time:

Average Rate = (R₁ + R₂)/2

Example

Equal sums at 8% and 12%:

Average Rate
= (8 + 12)/2
= 10%

30. Equal Simple Interest Condition

If two investments earn equal Simple Interest:

P₁R₁T₁ = P₂R₂T₂

Therefore:

P₁/P₂
= (R₂T₂)/(R₁T₁)

This is useful in ratio-based questions.

31. Principal Ratio for Equal Interest

If time is the same:

P₁R₁ = P₂R₂

Therefore:

P₁ : P₂ = R₂ : R₁

Example

Two sums earn equal SI at 10% and 15% for the same time.

P₁ : P₂
= 15 : 10
= 3 : 2

The amount invested at the lower rate must be larger.

32. Rate Ratio for Equal Interest

If principal and time differ:

R₁ : R₂
= P₂T₂ : P₁T₁

This follows from:

P₁R₁T₁ = P₂R₂T₂

33. Simple Interest vs Compound Interest

The main difference:

Simple Interest

Interest is calculated only on the original principal.

SI = PRT/100

Compound Interest

Interest is calculated on principal plus accumulated interest.

For annual compounding:

A = P(1 + R/100)^T

For one year:

SI = CI

when the principal and annual rate are the same.

For more than one year, Compound Interest is normally greater than Simple Interest when the rate is positive.

34. Difference Between CI and SI for 2 Years

For the same principal P and annual rate R%:

CI − SI
= P(R/100)²

or:

CI − SI
= PR²/10000

Example

P = ₹10,000 R = 10%

Difference
= 10000 × 10² /10000
= ₹100

This shortcut applies to 2 years with annual compounding at the same rate.

35. Fast Percentage Method

If:

P = 100

then:

SI = R × T

This makes percentage-only questions easier.

Example

Rate = 8% Time = 5 years

Assume:

P = 100

Then:

SI = 8 × 5
   = 40

So:

Amount = 140

Therefore:

P : A = 100 : 140
      = 5 : 7

36. One-Minute Revision Table

37. Common Exam Mistakes

1. Not Converting Months into Years

For 6 months:

T = 6/12 = 1/2 year

Do not use T = 6 in the standard annual formula.

2. Adding Interest to the Principal Every Year

That would introduce compounding.

Under Simple Interest:

Interest is calculated on the original principal only.

3. Confusing Interest with Amount

SI = Interest only

while:

Amount = Principal + Interest

4. Forgetting “Per Annum”

A rate such as 10% p.a. means 10% per year.

5. Using the Double-Money Shortcut for Compound Interest

T = 100/R

is the exact doubling relation for Simple Interest, not the general Compound Interest formula.

6. Ignoring the Time Difference Between Two Amounts

If amounts after 3 and 7 years are given, their difference represents interest for:

7 − 3 = 4 years

not 7 years.

7. Averaging Rates Directly for Unequal Investments

For unequal principal amounts, use the weighted average:

Average Rate = Σ(PR)/ΣP

A simple arithmetic average works only when the invested amounts are equal and the time periods are the same.

38. Exam Quick Tips

• Memorise SI = PRT/100 first; most other formulas can be derived from it.
• If only percentages or ratios are given, assume Principal = 100.
• Under SI, yearly interest remains constant.
• For months, divide the time by 12.
• For two different amounts at different years, use their difference to find yearly interest.
• If money doubles under SI, remember RT = 100.
• If money triples, remember RT = 200.
• For equal-interest questions, use P₁R₁T₁ = P₂R₂T₂.
• Keep Principal, Interest, and Amount separate while solving.
• Check whether the question asks for SI or the final Amount.

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