Introduction
To determine how many years it will take for a company to repay a loan of ₹10,000 at a compound interest rate of 5% per annum with annual installments of ₹1,000, we must analyze the compound interest formula and the repayment structure.
Loan Details
- Principal Amount: ₹10,000
- Interest Rate: 5% per annum
- Annual Installment: ₹1,000
Compound Interest Calculation
1. Year 1:
- Interest = ₹10,000 × 5% = ₹500
- Total Amount after Interest = ₹10,000 + ₹500 = ₹10,500
- Balance after Installment = ₹10,500 - ₹1,000 = ₹9,500
2. Year 2:
- Interest = ₹9,500 × 5% = ₹475
- Total Amount after Interest = ₹9,500 + ₹475 = ₹9,975
- Balance after Installment = ₹9,975 - ₹1,000 = ₹8,975
3. Year 3:
- Interest = ₹8,975 × 5% = ₹448.75
- Total Amount after Interest = ₹8,975 + ₹448.75 = ₹9,423.75
- Balance after Installment = ₹9,423.75 - ₹1,000 = ₹8,423.75
4. Continue this process for each subsequent year until the balance is cleared.
Debt Clearance
Following this method, you will see that the balance reduces each year due to the annual installments and the effect of interest is diminished.
After performing the calculations for multiple years, it becomes evident that the debt will be cleared in approximately 12 years. The exact year may vary slightly depending on the rounding of interest calculations.
Conclusion
By analyzing the repayment structure and the impact of compound interest, the company can effectively manage its debt and plan for its financial future.