Simple Interest

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💰 Discrete Interest - The Basics

Simple way to calculate interest on loan or investment!

📚 What is separate interest?

Simple Interestis the interest calculated on the principal only.

🎯 Important Note:
You get the same amount of interest every year.
Interest = Principal × Interest Rate × Duration

⭐ Key Terms

artifice	English	Code	Explanation
Original	Principal	P	Amount to be borrowed / invested
Interest rate	Rate of Interest	R	What is the percentage interest per annum (% per annum)
Period	Time	T	How many years/months/days?
separate interest	Simple Interest	SI	Amount of interest earned
sum	Amount	A	Principal + Interest = Total Amount

📐 Basic formula

SI = P × R × T / 100

Compound Interest = Principal × Rate × Duration / 100

A = P + SI

Amount = Principal + Separate Interest

🕐 Time change

was given	Convert to year	example
months	T = Months / 12	6 months = 6/12 = 0.5 year
days	T = days / 365	73 day = 73/365 = 1/5 year
weeks	T = Weeks / 52	26 weeks = 26/52 = 0.5 year

📊 Simple understanding - example

Question:If ₹1000 is kept at 5% interest for 3 years, what is the interest?

Solution:

P = ₹1000, R = 5%, T = 3 years
SI = P × R × T / 100
SI = 1000 × 5 × 3 / 100
SI = 15000 / 100 =₹150

Amount (A):1000 + 150 =₹1150

📈📉 Separate interest vs compound interest

Separate Interest (SI)	Compound Interest (CI)
Interest on principal only	Interest on principal + interest
The interest is equal every year	Interest increases every year
SI = PRT/100	CI = P(1+R/100)^n - P
Easy to calculate	Complicated

🎯 Important Notes

per annum (p.a.)= per annum
per month= per month
Interest rate is alwaysas an annual ratewill be given
Always on timeConvert to yearCalculate
Note that Amount = Principal + Interest

📐 Discrete Interest - Key Formulas

All Formulas Essential for TNPSC Exam!

🔢 Basic formulas

to find out	formula
Separate Interest (SI)	SI = (P × R × T) / 100
Amount (A)	A = P + SI = P(1 + RT/100)
Original (P)	P = (100 × SI) / (R × T)
Ratio (R)	R = (100 × SI) / (P × T)
Period (T)	T = (100 × SI) / (P × R)

📊 Amount based formulas

condition	formula
Principal from amount	P = (100 × A) / (100 + RT)
SI from sum	SI = A - P
Amount to ratio	R = (A – P) × 100 / (P × T)

💰 Double / Triple Formulas

condition	formula	Explanation
to double	T = 100 / R	Time to double the original
to triple	T = 200 / R	Time to triple the original
be n times	T = (n-1) × 100 / R	The period becomes n times the original

💡 Memory:Double = 100/R, Triple = 200/R, Quadruple = 300/R

🔄 Installment formulas

Type	formula
annual installment	P = x × n - SI (SI of all installments) SI = x × R × [n(n-1)/2] / 100
direct formula	x = P × (100 + nR/2) / (n × 100) x = installment amount

Type

formula

annual installment

P = x × n - SI (SI of all installments)

SI = x × R × [n(n-1)/2] / 100

direct formula

x = P × (100 + nR/2) / (n × 100)

x = installment amount

📈 Different rate/period formulas

condition	formula
Different rates	SI = P × (R₁T₁ + R₂T₂ + R₃T₃) / 100 (period T₁ at ratio R₁, period T₂ at ratio R₂...)
Different originals	SI = R × T × (P₁ + P₂ + P₃) / 100 (Same rate, same tenure, different principal)

🔀 True Discount formulas

artifice	formula
True Discount (TD)	TD = (A × R × T) / (100 + RT)
Present Worth (PW)	PW = (100 × A) / (100 + RT)
Communication	TD = A - PW = SI on PW

📋 Formula summary

To find SI:PRT/100
To find P:100×SI/(RT)
To find R:100×SI/(PT)

To find T:100×SI/(PR)
To find A:P + SI
Double T:100/R

📝 Separate Interest – 10 Key Examples

Frequently Asked Question Types in TNPSC Exam!

📌 Example 1: Basic SI Calculation

Question:If ₹5000 is kept for 4 years at 8% interest rate, what is the compound interest earned?

Solution:
P = ₹5000, R = 8%, T = 4 years

SI = P × R × T / 100
SI = 5000 × 8 × 4 / 100
SI = 160000 / 100 = ₹1600

Answer: ₹1600

📌 Example 2: Calculation of sum

Question:What is the amount of ₹8000 deposited for 3 years at 10% interest rate?

Solution:
P = ₹8000, R = 10%, T = 3 years

SI = 8000 × 10 × 3 / 100 = ₹2400

Sum A = P + SI
A = 8000 + 2400 = ₹10400

Answer: ₹10,400

📌 Example 3: Original invention

Question:A sum yields ₹600 interest in 4 years at 5% interest. How much is the original?

Solution:
SI = ₹600, R = 5%, T = 4 years

Formula: P = (100 × SI) / (R × T)

P = (100 × 600) / (5 × 4)
P = 60000 / 20 = ₹3000

Answer: ₹3000

📌 Example 4: Finding Interest Rate

Question:A principal of ₹4000 gives ₹1000 interest in 5 years. What is the interest rate?

Solution:
P = ₹4000, SI = ₹1000, T = 5 years

Formula: R = (100 × SI) / (P × T)

R = (100 × 1000) / (4000 × 5)
R = 100000 / 20000 = 5%

Answer: 5%

📌 Example 5: Finding the period

Question:How many years will it take for ₹6000 principal to yield ₹1440 interest at 8% interest?

Solution:
P = ₹6000, R = 8%, SI = ₹1440

Formula: T = (100 × SI) / (P × R)

T = (100 × 1440) / (6000 × 8)
T = 144000 / 48000 = 3 years

Answer: 3 years

📌 Example 6: Doubling period

Question:How many years will it take for a sum to double at 10% interest rate?

Solution:
R = 10%

Double formula: T = 100 / R

T = 100 / 10 = 10 years

Answer: 10 years

📌 Example 7: Tripling period

Question:How many years will it take to triple ₹5000 at 8% interest rate?

Solution:
R = 8%

Triple formula: T = 200 / R

T = 200 / 8 = 25 years

Answer: 25 years

📌 Example 8: SI in months

Question:If ₹12000 is kept for 9 months at 6% interest, what is the interest?

Solution:
P = ₹12000, R = 6%, T = 9 months = 9/12 = 3/4 year

SI = P × R × T / 100
SI = 12000 × 6 × (3/4) / 100
SI = 12000 × 6 × 3 / (100 × 4)
SI = 216000 / 400 = ₹540

Answer: ₹540

📌 Example 9: Principal from sum

Question:A sum becomes ₹7200 in 4 years at 5% interest. What is original?

Solution:
A = ₹7200, R = 5%, T = 4 years

Formula: P = (100 × A) / (100 + RT)

P = (100 × 7200) / (100 + 5 × 4)
P = 720000 / 120 = ₹6000

Answer: ₹6000

📌 Example 10: Different proportions

Question:₹10000 principal is kept at 5% for the first 2 years and 8% for the next 3 years. How much is the total interest?

Solution:
P = ₹10000

SI for first 2 years = 10000 × 5 × 2 / 100 = ₹1000
Next 3 years SI = 10000 × 8 × 3 / 100 = ₹2400

Total SI = 1000 + 2400 = ₹3400

Answer: ₹3400

📊 Important notes

In SI questions P, R, T, SI, A - if you know 3 of these you can find the rest
Divide by 12 to convert months to years
Note that double = 100/R, triple = 200/R
Remember that Amount = Principal + Interest

⚡ Separate Interest - Crossroads

Super Tricks to Save Time in TNPSC Exam!

🚀 Trick 1: 1% - 1 Year Quick Method

1 year SI = P/100 at 1% interest per rupee

Hence SI = P × R × T / 100 for T year at R% interest

Example:2 year SI at 4% interest for ₹500

1% - 1 year = 500/100 = 5

4% - 2 year = 5 × 4 × 2 =₹40

🚀 Trick 2: Double quick formula

n times T years but:

R = (n - 1) × 100 / T
T = (n - 1) × 100 / R

times	Period (T)
double (2x)	100/R
Triple (3x)	200/R
Four times (4x)	300/R
Five times (5x)	400/R

🚀 Trick 3: Dividing SI into Ratios

SI : P = R × T : 100

Interest and principal will be in the ratio of R×T : 100

Example:4 years at 5% interest

SI : P = 5×4 : 100 = 20 : 100 =1 : 5

If principal is ₹5000, then SI = 5000/5 =₹1000

🚀 Trick 4: Amount Quick Calculation

A = P × (100 + RT) / 100

Or

A : P = (100 + RT) : 100

Example:₹2000, 5%, 4 yrs

A = 2000 × (100 + 20) / 100 = 2000 × 120/100 =₹2400

🚀 Trick 5: Quick way to find the original

If amount A, rate R, period T are known:

P = A × 100 / (100 + RT)

Example:A = ₹1320, R = 8%, T = 2 years

P = 1320 × 100 / (100 + 16) = 132000/116 =₹1137.93

🚀 Trick 6: RT multiplication memory

SI% = R × T

What percentage of principal is interest = R × T

Example:6 years at 5% interest = 30% interest on principal

SI for ₹8000 = 8000 × 30% =₹2400

🚀 Trick 7: Principal on interest difference

If difference of interest in two rates = D:

P = D × 100 / [(R₁ - R₂) × T]

Example:₹600 is the difference in 2-year interest at 5% and 8%

P = 600 × 100 / [(8-5) × 2] = 60000/6 =₹10000

🚀 Trick 8: Quick change of month / day

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
73 days	= 1/5 year
146 day	= 2/5 years

🚀 Trick 9: Rule of 72

Approximately double:

T ≈ 72 / R(for CI)
T = 100 / R(for SI)

Example:Double at 8% SI

T = 100/8 =12.5 years

🚀 Trick 10: SI and A relationship

If SI is known A:A = P + SI
If A is known SI:SI = A - P
If A and SI are known P:P = A - SI

Shortcut:Note that A = P(1 + RT/100).

📊 TNPSC Frequently Asked Categories

Question type	Crossroads
Calculate SI	P × R × T / 100
Find the original	100 × SI / (R × T)
Find the ratio	100 × SI / (P × T)
Double period	100 / Rs
Principal in amount	A × 100 / (100 + RT)

💡 Important memory tips

SI = PRT/100- Basic formula
A = P + SI- Amount = Principal + Interest
Double T = 100/R- Quick formula
SI% = R × T- How much % interest on principal
Month → Year:Divide by 12
Day → Year:Divide by 365

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