Math Problem Statement

Determine the amount of equal payment to be made for a loan of 2,00,000 taken fora period of 4 years at 10% rate of interest.

Solution

To determine the equal payment for the loan, we use the formula for Equated Monthly Installment (EMI), which is typically calculated using the following formula:

EMI=Pr(1+r)n(1+r)n1EMI = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}

Where:

  • PP = Principal amount (loan) = ₹2,00,000
  • rr = Monthly interest rate = Annual interest rate / 12 = 10% / 12 = 0.10 / 12 = 0.00833
  • nn = Number of months = 4 years × 12 = 48 months

Let's calculate the EMI using this formula.The equal monthly payment (EMI) for the loan of ₹2,00,000 over a period of 4 years at an interest rate of 10% is approximately ₹5,072.52.

Would you like more details or have any questions about this calculation?

Here are 5 related questions:

  1. What would the EMI be if the loan period was extended to 5 years?
  2. How much total interest will be paid over the 4-year period?
  3. How does the EMI change with a 12% interest rate?
  4. Can you calculate the total amount paid over the loan's duration?
  5. How does increasing the loan amount to ₹3,00,000 affect the EMI?

Tip: A lower interest rate or a longer loan period can reduce the EMI, but you'll end up paying more in total interest over time.

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Math Problem Analysis

Mathematical Concepts

Loan Amortization
Equated Monthly Installment (EMI)
Simple Interest and Compound Interest

Formulas

EMI = [P * r * (1 + r)^n] / [(1 + r)^n - 1]
Monthly Interest Rate = Annual Interest Rate / 12
n = Loan Period in Years × 12

Theorems

Loan Amortization Formula

Suitable Grade Level

Grades 10-12