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Unit: Basic Algebra
Chapter: Simple Interest & Unitary Method
Reference: – Introduction to Simple Interest, Principal (P), Rate (R), Time (T), Simple Interest Formula (I = PRT/100), Amount (A = P + I), Finding Principal, Rate or Time, Unitary Method (Finding Value of One Unit), Direct and Inverse Variation, Applications of Unitary Method, Real-Life Problems
After studying this chapter, you should be able to understand:
- Introduction to Simple Interest & Its Meaning
- Principal, Rate, Time and Amount
- Simple Interest Formula & Its Applications
- Finding Principal, Rate or Time When Other Values Are Given
- Unitary Method: Finding the Value of One Unit
- Direct and Inverse Variation by Unitary Method
- Real-Life Applications of Simple Interest & Unitary Method
We often borrow small amounts of money from our friends to eat out or to purchase books. However, when we need to purchase a house or a car we need large amounts of money. In such cases, we resort to banks or moneylenders.
Unlike our friends, they charge us an extra amount for lending us the money. This extra amount we pay for using their money is called interest.
We also deposit money in a bank for safe keeping. Here, the bank uses our money and hence gives us interest on it.
What are the factors affecting calculation of interest??
The interest depends upon-
- Principal (P) – The money that we borrow or deposit is called the principal or sum.
- Time Period (T) – The duration for which money is borrowed or deposited is called time. It is always in years, but if you are given monthly interest rates then always convert to the yearly measure.
- Rate of Interest (R) – The interest paid per annum, i.e., yearly on the borrowed or deposited money.
This interest is called as simple interest which is calculated on the principal for the duration of the money borrowed or deposited at a given rate of interest.
The money that is paid back or returned at the end of the time period is called the total amount.
Total Amount = Principal + Interest
Or Principal = Total Amount – Interest
Or Interest = Total Amount – Principal
Examples:
1. Find the amount payable if interest on Rs. 10000 borrowed is Rs. 150.
Solution
Principal = Rs. 10000
Interest = Rs. 150
Amount = Principal + Interest
= Rs. 10000 + 150
= Rs. 10150
So, the amount to be repaid is Rs. 10150.
2. Find the interest on Rs. 8200 borrowed if the amount repaid is Rs. 8500.
Solution
Principal = Rs. 8200
Amount = Rs. 8500
Interest = Amount – Principal
= Rs. 8500 – 8200
= Rs. 300
So, the interest on money borrowed is Rs. 300.
Computing Simple Interest, Using Interest Rate
Simple Interest = P × R ×T100
Source: Kapdec.com
where P = Principal or the sum borrowed
R = Rate of interest charged on sum borrowed per annum
(in %)
T = Time for which sum is borrowed
Example:
3. Ronald takes a loan of Rs 10,000 from a bank for a period of 1 year. The rate of interest is 10% per annum. Find the interest and the amount he has to the pay at the end of a year.
Solution:
Here, the loan sum = P = Rs 10,000
Rate of interest per year = R = 10%
Time for which it is borrowed = T = 1 year
Thus, simple interest for a year, SI=P × R × T100
Source: Kapdec.com
= (10,000×10× 1)/100 =Rs1,000
Amount that Ronald has to pay to the bank at the end of the year = Principal + Interest = 10,000 + 1,000 = Rs 11,000
4. Joshua pays Rs7,000 as an amount on the sum of Rs5,000 that he had borrowed for 2 years. Find the rate of interest.
Solution:
Amount, A = Rs 5000
Principal, P = Rs 7000
Simple Interest, SI = A – P = 7000 – 5000 = Rs 2000
Time, T = 2 years
Rate of Interest, R = ?
Now, SI=P × R × T100
Source: Kapdec.com
⇒R=SI×100P × T
Source: Kapdec.com
⇒R= (2000× 100)/(7000 × 2)=14.29
Thus R = 14.29%
