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To calculate the total interest, monthly interest, and monthly premium under the diminishing balance method, follow these steps:
1. Calculate Monthly Interest Rate
The annual interest rate is 20%, so the monthly interest rate is:
\text{Monthly Interest Rate} = \frac{20\%}{12} = 1.67\%Monthly Interest Rate=1220%=1.67%
2. Calculate Monthly Payment (EMI)
The formula for the monthly payment (EMI) under the diminishing balance method is:
\text{EMI} = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1}EMI=(1+r)n−1P×r×(1+r)n
Where:
- ( P ) is the principal amount (20,000)
- ( r ) is the monthly interest rate (0.0167)
- ( n ) is the number of installments (10)
Plugging in the values:
\text{EMI} = \frac{20000 \times 0.0167 \times (1 + 0.0167)^{10}}{(1 + 0.0167)^{10} - 1}EMI=(1+0.0167)10−120000×0.0167×(1+0.0167)10
3. Calculate Monthly Interest and Principal Repayment
For each month, the interest is calculated on the remaining principal balance. The principal repayment is the EMI minus the interest.
4. Calculate Total Interest Paid
Sum up the interest paid each month over the 10 installments.
Example Calculation
Let’s break down the first few months as an example:
Month 1:
- Interest: ( 20000 \times 0.0167 = 334 )
- Principal Repayment: ( \text{EMI} - \text{Interest} )
- Remaining Principal: ( 20000 - \text{Principal Repayment} )
Month 2:
- Interest: ( \text{Remaining Principal} \times 0.0167 )
- Principal Repayment: ( \text{EMI} - \text{Interest} )
- Remaining Principal: ( \text{Previous Remaining Principal} - \text{Principal Repayment} )
Repeat this process for all 10 months.
