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Message: <blockquote data-quote="Mr.Wikirana" data-source="post: 29963019" data-attributes="member: 584253"><p>AI Support                                 </p><p> </p><p></p><p>To calculate the total interest, monthly interest, and monthly premium under the diminishing balance method, follow these steps:</p><h3>1. <strong>Calculate Monthly Interest Rate</strong></h3><p>The annual interest rate is 20%, so the monthly interest rate is:</p><p>\text{Monthly Interest Rate} = \frac{20\%}{12} = 1.67\%Monthly Interest Rate=1220%=1.67%</p><h3>2. <strong>Calculate Monthly Payment (EMI)</strong></h3><p>The formula for the monthly payment (EMI) under the diminishing balance method is:</p><p>\text{EMI} = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1}EMI=(1+r)n−1P×r×(1+r)n</p><p>Where:</p><ul> <li data-xf-list-type="ul">( P ) is the principal amount (20,000)</li> <li data-xf-list-type="ul">( r ) is the monthly interest rate (0.0167)</li> <li data-xf-list-type="ul">( n ) is the number of installments (10)</li> </ul><p>Plugging in the values:</p><p>\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</p><h3>3. <strong>Calculate Monthly Interest and Principal Repayment</strong></h3><p>For each month, the interest is calculated on the remaining principal balance. The principal repayment is the EMI minus the interest.</p><h3>4. <strong>Calculate Total Interest Paid</strong></h3><p>Sum up the interest paid each month over the 10 installments.</p><h3>Example Calculation</h3><p>Let’s break down the first few months as an example:</p><h4>Month 1:</h4> <ul> <li data-xf-list-type="ul"><strong>Interest</strong>: ( 20000 \times 0.0167 = 334 )</li> <li data-xf-list-type="ul"><strong>Principal Repayment</strong>: ( \text{EMI} - \text{Interest} )</li> <li data-xf-list-type="ul"><strong>Remaining Principal</strong>: ( 20000 - \text{Principal Repayment} )</li> </ul><h4>Month 2:</h4> <ul> <li data-xf-list-type="ul"><strong>Interest</strong>: ( \text{Remaining Principal} \times 0.0167 )</li> <li data-xf-list-type="ul"><strong>Principal Repayment</strong>: ( \text{EMI} - \text{Interest} )</li> <li data-xf-list-type="ul"><strong>Remaining Principal</strong>: ( \text{Previous Remaining Principal} - \text{Principal Repayment} )</li> </ul><p>Repeat this process for all 10 months.</p><h3></h3></blockquote><p></p>

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