Understanding Compound Interest
Compound interest is the interest calculated on the initial principal, which also includes all the accumulated interest from previous periods. This is different from simple interest, where interest is calculated only on the principal.
Formula for Compound Interest
The formula to calculate compound interest is:
A = P (1 + r/n)^(nt)
Where:
- A = the amount of money accumulated after n years, including interest.
- P = principal amount (initial investment).
- r = annual interest rate (decimal).
- n = number of times that interest is compounded per year.
- t = number of years the money is invested or borrowed.
For this problem:
- P = Rs. 15625
- r = 4% = 0.04
- n = 1 (compounded annually)
- t = 3 years
Calculation Steps
1. Calculate the amount after 3 years:
A = 15625 * (1 + 0.04/1)^(1*3)
A = 15625 * (1 + 0.04)^3
A = 15625 * (1.04)^3
A = 15625 * 1.124864
2. Final Amount:
A ≈ 17500
Calculate Compound Interest
To find the compound interest, subtract the principal from the total amount:
Compound Interest = A - P
Compound Interest = 17500 - 15625
Compound Interest = Rs. 1875
Conclusion
Thus, the compound interest on Rs. 15625 for 3 years at an interest rate of 4% per annum, compounded annually, is Rs. 1875.