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When money is borrowed from some bank or agency or any individual, then while returning the money the borrower has to pay some additional amount along with the principal amount at the end of the specified period. The additional amount that the borrower pays to the lender (borrowed money from) is called the Interest.
The interest can be characterised as simple interest or compound interest. Before going to the difference between simple interest and compound interest, let us learn some basic terminology to understand Simple and compound interest better.
| Table of Content |
Key Terms: Simple Interest, Compound Interest, Principal, Amount, Rate, Time, Difference between simple interest and compound interest
Some definitions
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- Principal: The money borrowed by the borrower.
- Interest: The additional money that borrower pays to the lender for using money.
- Amount: The total money that borrower pays back to the lender at the end of a specified period of time.
Amount = Principal + Interest or Interest = Amount – Principal
Or
A = P + I
Where A= Amount
P = Principal
I = Interest
Also Read: Ratio to Percentage
Simple Interest
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If the interest is calculated uniformly throughout the loan period the principal is called simple interest.
If, P is the principal and the interest rate is R% per annum
Then Interest on Rs P for T years is = P x R x T /100
Example: Richa borrowed a sum of Rs. 4000 for 5 years at the rate of 15% per annum. Find the interest.
Solution: Interest (I) = P x R x T /100
Where P = Rs. 4000 R = 15% T = 5 years
Interest = 4000 x 15 x 5 /100
Interest = 3000 Rs
Also Read: Compound Interest
Compound Interest
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If the borrower and lender, fixed a certain interval of time to return the money. The interest is calculated on the principal amount as well as on the interest gained on the principal amount. This is called compound interest.
Conversion Period:
A new term is introduced here is called conversion period. The conversion period is the fixed interval of time at the end of which interest is calculated and then added to the principal to calculate the compound interest.
The formulae for calculating the compound Interest:
Case1- When the interest is compounded annually:
A = P (1+ R/100)n
Case2- When the interest is compounded half-yearly:
A = P (1 + R/2x100)2n
Case3- When the interest is compounded quarterly:
A = P (1 + R/4x100)4n
Example: Find the amount of Rs 8000 for 3 years, compounded annually at 10% per annum.
Solution:
Formula for compound Interest:
A = P (1+ R/100)n
A = 8000(1+ 10/100)3
A= 8 x 11x 11 x 11
A = Rs 10648
Applications of Compound Interest Formula:
The compound interest formula can be used in the following cases:
- Increase or decrease in population
- Calculating the growth of bacteria when the rate of growth is known
- Depreciation in the machine value when the rate is given
Also Read: Area of square using diagonal
Difference Between Compound Interest and Simple interest
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The following table enlists the key differences between Simple Interest and Compound Interest:
| Simple Interest | Compound Interest |
| 1. Compound Interest is calculated on the principal amount and the interest earned when the conversion period is known. |
| 2. Compound interest depends upon both the principal amount and previous interest earned. |
| 3. Returns are very high in the case of compound interest. |
| 4. In compound interest the amount at the end of the first year is principal for next year. |
| 5. In compound interest the interest rate varies. |
Example:
Let’s understand the difference between Simple and compound interest using an example:
Principal = Rs100
Interest Rate: 10% per Anum
Time = 5 years
| Initial Deposit | Simple Interest | Compound Interest |
| 1st Year | P = 100, R = 10, T =1 Simple Interest = 10 | P= 100, R = 10, T= 1 Compound Interest = Amount – Principal A =110 Compound Interest = 110- 100 = 10 |
| 2nd Year | P = 100, R = 10, T =1 Simple Interest = 10 | P= 110, R = 10, T= 1 A= 121 Compound Interest = 121- 110 = 11 |
| Total Interest | 10 + 10 = 20 | 10 + 11 = 21 |
| Interest calculation using the formula | SI = P x R x T /100 = 100 x 10 x 2 /100 = Rs 20 | CI = A- P A = P (1 + R/100)n = 100 (1 + 10/100)2 = 11 x 11 = 121 CI = 121- 100 = Rs 21 |
Points to Remember
- Simple interest benefits the consumers who pay their loan
- The compound interest is dependent upon the amount at the end of the previous tenure instead of the principal amount.
- Bank, insurance companies charge compound interest.
- The other terms used for the time duration are per annum, annual or per year, semi-annual, half-yearly, or quarterly. Per annum, annual or per year means over a period of one year, quarterly means over a period of 3 months, and semi-annual means the duration of 6 months.
Also Read: Unit Conversion
Sample Questions
Q1- A sum of Rs 800 is lent for one year at the rate of 18% per annum. Find the interest? (3 marks)
Solution:
Formula of Simple Interest = I = P x R x T /100
Principal =P = 800 R= Rate of Interest = 18 % Time = T = 1 year
I = 800 x 18 x 1 /100
= 8 x 18 = Rs 144 – Ans
Q2- In how many years will Rs 750 amount to Rs 900 at 4 % per annum? (3 marks)
Solution:
A= Rs 900 P = Rs 750 R = 4 % T =?
Formula for Simple Interest = P x R x T /100
Simple Interest = Amount – Principal
S I = 900 – 750
= Rs 150
150 = 750 x 4x T /100
T = 150 x 100 /750 x 4
= 5 Years – Ans
Q3- What will be the compound interest on Rs 4000 in two years when the rate of interest is 5% per annum? (3 marks)
Solution:
The formula of Compound Interest
A = P (1 + R/100)n
Compound Interest = Amount – Principal
A = 4000 (1 + 5/100)2
= 4000 x 105/100 x 105/100
= 4 x 105 x 105 /10
= 4410
Compound Interest = 4410 – 4000
= Rs 410
Q4- Find the difference between the simple interest and the compound interest on Rs 5000 for 2 years at 5% per annum. (5 marks)
Solution:
Given,
P = 5000
T = 2 Years
R = 5%
Formula of Simple Interest = Px R x T /100
= 5000 x 5 x 2 /100
= Rs 500
Formula of Compound Interest =
A = P ( 1 + R/100)n
= 5000 ( 1 + 5 /100)2
= 5000 x 105/100 x 105/100
= 5 x 105x 105 /10
= Rs 5512.5
Amount = 5512.5
Principal = 5000
Interest = Amount – Principal
= 5512.5 – 5000
= Rs 512.5
Difference between Compound Interest &Simple Interest = 512.5 – 500
= Rs 12.5 – Ans
Q-5 – Find the difference between the simple interest and compound interest on 2500 for 2 years at 10% per annum. (3 marks)
Solution:
Formula for simple interest = P x R x T /100
Formula for Compound Interest = A = P ( 1 + R/100)n
Given,
P = 2500
R = 10%
T or n = 2 years
Simple Interest = 2500 x 10 x 2 /100
= 500
Compound Interest = Amount- Principal
A = P (1 + R/100)n
= 2500 (1 + 10/100)2
= 2500x 110/100 x 110/100
= 25 x 121
= 3025
Compound Interest = 3025 – 2500
= 525
Difference between simple interest and compound interest = 525 -500
= Rs 25
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