A man takes a personal loan of ₹ 2,00,000 at an interest rate of 15% p.a. compounded monthly, to be repaid by equal monthly instalments in 4 years. Calculate the EMI, using reducing balance method. [Given : (1⋅0125)−48=0⋅55]
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Step-by-Step Solution
Step 1: Identify Given Values
First, we identify the principal amount (P), the monthly interest rate (r), and the total number of monthly installments (n). The annual interest rate is 15%, so we divide by 12 to get the monthly rate. The loan duration is 4 years, so we multiply by 12 to get the total number of months.
Step 2: Apply EMI Formula
We use the formula for calculating EMI (Equated Monthly Installment) for a loan based on the reducing balance method. This formula takes into account the principal amount, the monthly interest rate, and the total number of installments.
Step 3: Substitute Values into Formula
Now, we substitute the identified values of P, r, and n into the EMI formula. This sets up the equation for calculation.
Step 4: Simplify the Expression
We simplify the terms inside the formula. We know that (1+0.0125) is 1.0125. We are given that (1.0125)−48=0.55. To use this, we can rewrite (1.0125)48 as 1/(1.0125)−48=1/0.55.
Step 5: Calculate (1.0125)48
Using the given value, we calculate (1.0125)48 by taking the reciprocal of 0.55. This gives us approximately 1.81818.
Step 6: Complete the EMI Calculation
Now, we substitute the calculated value of (1.0125)48 back into the EMI formula and perform the final arithmetic operations to find the EMI.