Understanding Compound Interest
To find the principal sum (P) on which the compound interest (CI) is calculated, we can use the formula for compound interest:
CI = P * [(1 + r/n)^(nt) - 1]
Where:
- CI = Compound Interest
- P = Principal amount (the sum we want to find)
- r = Rate of interest per annum (as a decimal)
- n = Number of times interest applied per time period
- t = Time in years
Given:
- CI = 164
- r = 5% = 0.05
- n = 1 (compounded annually)
- t = 2 years
Calculating the Principal Amount
1. Rearranging the formula to find P:
P = CI / [(1 + r/n)^(nt) - 1]
2. Substitute the known values:
P = 164 / [(1 + 0.05/1)^(1*2) - 1]
3. Calculate:
- (1 + 0.05) = 1.05
- (1.05)^2 = 1.1025
- 1.1025 - 1 = 0.1025
4. Substitute back to find P:
P = 164 / 0.1025
5. Final calculation:
P ≈ 1600
Conclusion
The principal sum on which the compound interest of rupees 164 at a rate of 5% per annum for 2 years, compounded annually, is approximately rupees 1600.
This calculation demonstrates how compound interest accumulates over time, and understanding this formula is crucial for financial planning and investment decisions.