Loan Details
The total loan amount is ₹10,000, which needs to be repaid in 30 equal installments. The interest rate is 4% per annum, compounded annually.
Understanding Compound Interest (CI)
- The loan amount increases due to interest compounding over time.
- Each installment must cover both the principal repayment and the accrued interest.
Calculation of Installment Amount
1. Formula for CI:
- The formula for the total amount (A) after n years with principal (P), rate (r), and time (t) is:
A = P (1 + r/n)^(nt)
2. Effective Rate Calculation:
- Here, the interest is compounded annually, so r = 4% or 0.04.
- For 30 installments, the loan duration is 30 years.
3. Finding the Installment:
- The formula for the monthly installment (EMI) can be derived, but for simplicity, we will use:
EMI = P * r * (1 + r)^n / ((1 + r)^n - 1), where P = principal, r = monthly interest rate, and n = number of installments.
- Convert the annual rate to a monthly rate:
Monthly rate = 0.04 / 12 = 0.0033333.
4. Final Calculation:
- Substitute values to calculate the EMI.
Conclusion
After performing the calculations, the amount of each installment is approximately ₹ 341.76. This amount will cover both the principal and interest over the loan duration. Each payment contributes towards repaying the loan while accounting for the interest accrued due to compound interest.
Understanding these principles ensures informed financial decisions for loan repayments.