Understanding Compound Interest
When dealing with loans, it's essential to understand how compound interest works. Compound interest means that interest is calculated on the initial principal and also on the accumulated interest from previous periods.
Loan Details
- Principal Amount: ₹2000
- Rate of Interest: 10% per annum
- Time Period: 3 years
Formula for Compound Interest
The formula to calculate the total amount (A) after n years with compound interest is:
A = P (1 + r/n)^(nt)
Where:
- A = the amount of money accumulated after n years, including interest.
- P = principal amount (the initial loan).
- r = annual interest rate (decimal).
- n = number of times that interest is compounded per year.
- t = number of years the money is borrowed for.
In our case, since the interest is compounded annually:
- P = 2000
- r = 10/100 = 0.10
- n = 1 (compounded once a year)
- t = 3
Calculating Total Amount
Plugging in the values:
A = 2000 (1 + 0.10/1)^(1*3)
A = 2000 (1 + 0.10)^3
A = 2000 (1.10)^3
A = 2000 * 1.331
Thus, A = ₹2662.
Calculating Interest Paid
To find the interest paid, subtract the principal from the total amount:
Interest = A - P
Interest = 2662 - 2000
Interest = ₹662.
Conclusion
The interest paid after three years on a loan of ₹2000 at 10% p.a. compounded annually is ₹662. Understanding this concept is crucial for borrowers to manage their loans effectively.