Effective rate of interest

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Querist : Anonymous

Querist : Anonymous (Querist)

03 June 2014 How can we calculate effective rate of interest if interest is levied at diffferent rates as per slabs-
Let loan amt be rs.20 lakhs
Tenure of loan- 14 yrs or 168 months
Interest slab-
upto 7 lac- 8%
7 lac to 15 lac- 9%
15 lac to 20 lac- 10%

Querist : Anonymous

Querist : Anonymous (Querist)

04 June 2014 Please answer the query

Aashok Kumar Sharma online

Aashok Kumar Sharma online

(Expert)
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21 July 2024 To calculate the effective rate of interest when interest is levied at different rates across different slabs of the loan amount, we can use a weighted average approach. Here’s how you can calculate it step-by-step:

### Step 1: Calculate the Interest Payable in Each Slab

1. **Interest on the first slab (up to 7 lakhs)**:
- Loan amount in this slab = 7 lakhs
- Interest rate = 8%
- Interest payable = Loan amount * Interest rate = 7L * 8% = 56K

2. **Interest on the second slab (7 lakhs to 15 lakhs)**:
- Loan amount in this slab = 15 lakhs - 7 lakhs = 8 lakhs
- Interest rate = 9%
- Interest payable = Loan amount * Interest rate = 8L * 9% = 72K

3. **Interest on the third slab (15 lakhs to 20 lakhs)**:
- Loan amount in this slab = 20 lakhs - 15 lakhs = 5 lakhs
- Interest rate = 10%
- Interest payable = Loan amount * Interest rate = 5L * 10% = 50K

### Step 2: Calculate the Total Interest Payable

Total interest payable = Interest on first slab + Interest on second slab + Interest on third slab
= 56K + 72K + 50K
= 1,78,000

### Step 3: Calculate the Effective Rate of Interest

To find the effective rate of interest, we use the concept of weighted average interest rate based on the amounts and rates in each slab.

1. **Weight of each slab**:
- Slab 1 (up to 7 lakhs): 7L / 20L = 0.35
- Slab 2 (7 lakhs to 15 lakhs): 8L / 20L = 0.40
- Slab 3 (15 lakhs to 20 lakhs): 5L / 20L = 0.25

2. **Calculate weighted interest rates**:
- Weighted interest rate = (Interest on slab 1 * Weight of slab 1) + (Interest on slab 2 * Weight of slab 2) + (Interest on slab 3 * Weight of slab 3) / Total loan amount

- Weighted interest rate = (56K * 0.35 + 72K * 0.40 + 50K * 0.25) / 20L

3. **Compute the Effective Rate of Interest**:

- Effective rate of interest = Weighted interest rate * 100 / Total loan amount

- Effective rate of interest = (96,600 / 20L) * 100

- Effective rate of interest ≈ 4.83%

### Conclusion

The effective rate of interest for the given loan, considering the interest slabs and the amounts involved, is approximately 4.83% per annum. This method provides a more accurate representation of the overall cost of borrowing across different interest rate slabs than simply averaging the rates themselves.

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