Interest
What is Interest?
The initial sum of money borrowed or invested.
Key formula / rule: Simple Interest
Key points
- Understand the difference between Simple and Compound Interest.
- Calculate Simple Interest and the total amount.
- Calculate Compound Interest and the total amount for various compounding frequencies.
- Determine the principal, rate, or time period given other variables.
Common exam trap
Confusing SI and CI formulas.
Definitions
- Term
Principal (P)
- Meaning
The initial sum of money borrowed or invested.
- Term
Rate of Interest (R)
- Meaning
The percentage at which interest is charged or earned, usually per annum.
- Term
Time Period (T)
- Meaning
The duration for which the money is borrowed or invested, usually in years.
- Term
Simple Interest (SI)
- Meaning
Interest calculated only on the principal amount.
- Term
Compound Interest (CI)
- Meaning
Interest calculated on the principal amount and also on the accumulated interest of previous periods.
- Term
Amount (A)
- Meaning
The total sum after adding the interest to the principal.
Learning objectives
Understand the difference between Simple and Compound Interest.
Calculate Simple Interest and the total amount.
Calculate Compound Interest and the total amount for various compounding frequencies.
Determine the principal, rate, or time period given other variables.
Solve problems involving the difference between SI and CI.
Formulae
- Name
Simple Interest
- Note
P = Principal, R = Rate of Interest per annum, T = Time period in years.
- Expression
SI = (P × R × T) / 100
- Name
Amount (Simple Interest)
- Note
A = Total Amount after T years.
- Expression
A = P + SI
- Name
Compound Interest (Annual Compounding)
- Note
Calculates the total amount when interest is compounded annually.
- Expression
A = P (1 + R/100)T
- Name
Compound Interest (General)
- Note
n = number of × interest is compounded per year (e.g., n=2 for semi-annually, n=4 for quarterly).
- Expression
A = P (1 + R/(n×100))^(n×T)
- Name
Compound Interest Amount
- Note
Calculates the total compound interest earned.
- Expression
CI = A - P
- Name
Difference between CI and SI (2 years)
- Note
Useful for quickly finding the difference in interest over two years.
- Expression
Difference = P (R/100)2
Prerequisites
Basic Arithmetic (Addition, Multiplication, Division)
Percentage calculations
Fractions and Decimals
Basic Algebra (solving for variables)
Common mistakes
Confusing SI and CI formulas.
Incorrectly applying the compounding frequency (e.g., calculating annual CI for semi-annual compounding).
Not considering the time period correctly, especially when it's not a whole number of years.
Forgetting to add the interest to the principal to find the total amount.
Calculating interest on interest for SI.
Keywords
Simple Interest
Compound Interest
Principal
Rate
Time
Amount
Compounding Frequency
Interest Calculation
Financial Mathematics
Practice preview
What is the simple interest on a principal amount of Rs. 5000 at an annual interest rate of 10% for 3 years?…
easy
A sum of Rs. 12000 yields a simple interest of Rs. 3600 in 3 years. What is the annual rate of interest?…
medium
A debt of Rs. 6450 is due in 4 years at 5% simple interest. What is the annual installment that will discharge the debt?…
medium