Understanding Compound Interest
Compound interest is calculated on the initial principal and also on the accumulated interest from previous periods. This makes it a powerful tool for growing investments over time.
Given Data
- Principal Amount (P): 500 rupees
- Rate of Interest (R): 12% per annum
- Time (T): 1½ years (or 1.5 years)
Formula for Compound Interest
The formula for 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 = the number of years the money is invested for.
For simplicity, we will assume that interest is compounded annually (n = 1).
Calculating the Amount
1. Convert the interest rate into decimal:
- r = 12/100 = 0.12
2. Plug in the values into the formula:
- A = 500 * (1 + 0.12/1)^(1*1.5)
- A = 500 * (1 + 0.12)^(1.5)
- A = 500 * (1.12)^(1.5)
3. Calculate (1.12)^(1.5):
- (1.12)^(1.5) ≈ 1.1836 (approx)
4. Final calculation:
- A ≈ 500 * 1.1836 ≈ 591.80 rupees
Calculating Compound Interest
To find the compound interest (CI), subtract the principal from the total amount:
- CI = A - P
- CI ≈ 591.80 - 500 = 91.80 rupees
Conclusion
The compound interest on 500 rupees for 1½ years at a rate of 12% per annum is approximately 91.80 rupees.