To calculate the equal payments for a loan of Rs. 200,000 over 4 years at an interest rate of 10%, we need to use the formula for an installment loan (typically the annuity formula). The formula is as follows:

$EMI = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1}$

Where:

• $EMI$ = Equal Monthly Installment
• $P$ = Principal amount (loan amount)
• $r$ = Monthly interest rate (annual interest rate divided by 12)
• $n$ = Total number of payments (loan tenure in months)

Step-by-Step Calculation:

1. Principal (P) = Rs. 200,000
2. Annual Interest Rate = 10% (0.10 as a decimal)
3. Loan Period = 4 years (which is 48 months)

To find the monthly interest rate: $r = \frac{10\%}{12} = \frac{0.10}{12} = 0.008333$

The number of payments (n) for 4 years: $n = 4 \times 12 = 48 \text{ months}$

Now, applying the values to the EMI formula:

$EMI = \frac{200,000 \times 0.008333 \times (1 + 0.008333)^{48}}{(1 + 0.008333)^{48} - 1}$

Let's compute the EMI:

$EMI = \frac{200,000 \times 0.008333 \times (1.008333)^{48}}{(1.008333)^{48} - 1}$

I'll calculate this and provide the result.

Let me proceed. Given values P = 200000 # Principal amount in Rs. annual_interest_rate = 0.10 # Annual interest rate (10%) loan_years = 4 # Loan duration in years

Monthly interest rate

r = annual_interest_rate / 12

Total number of payments (months)

n = loan_years * 12

Calculating the EMI using the formula

EMI = (P * r * (1 + r)**n) / ((1 + r)**n - 1) EMIThe equal monthly payment (EMI) for the loan of Rs. 200,000 taken for 4 years at an interest rate of 10% is approximately Rs. 5,072.52.

Would you like more details on the calculation process, or do you have any further questions?

Here are some related questions you might find interesting:

1. How would the EMI change if the loan tenure was increased to 5 years?
2. What is the total interest paid over the course of the loan?
3. How would the EMI differ if the interest rate was 12% instead of 10%?
4. What is the effect of making early repayments on the total interest paid?
5. How can the EMI formula be applied to calculate the monthly payment for a car loan?

Tip: When calculating loans with interest, even small changes in the interest rate or loan tenure can lead to significant differences in the monthly payment.