Understanding Compound Interest
Compound interest is calculated on the initial principal and also on the accumulated interest from previous periods. This makes it different from simple interest, which 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 = the principal amount (initial investment).
- r = annual interest rate (decimal).
- n = number of times that interest is compounded per year.
- t = the number of years the money is invested for.
Given Values
- Principal (P) = RS. 2500
- Rate of Interest (r) = 4% per annum = 0.04 (as a decimal)
- Time (t) = 2 years
- Compounding Frequency (n) = 1 (annually)
Calculation Steps
1. Calculate the Total Amount (A):
- A = 2500(1 + 0.04/1)^(1*2)
- A = 2500(1 + 0.04)^2
- A = 2500(1.04)^2
- A = 2500 * 1.0816
- A = RS. 2704
2. Calculate Compound Interest (CI):
- CI = A - P
- CI = 2704 - 2500
- CI = RS. 204
Final Result
The compound interest on RS. 2500 for 2 years at a rate of 4% per annum is RS. 204.
This demonstrates how compound interest can significantly increase the value of an investment over time.