Sborrows ₹5,00,000 to buy a house. If he pays equal instalments for 20 years and 10% interest on outstanding balance what will be the equal annual instalment?

To calculate the equal annual installment for a loan of ₹5,00,000 at 10% interest over 20 years, we use the formula for the Equated Annual Installment (EAI) or the fixed installment amount. This is similar to calculating the Equated Monthly Installment (EMI) but on an annual basis.

The formula for the EAI is:

\[
\text{EAI} = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1}
\]

Where:
- \( P \) = Principal amount (₹5,00,000)
- \( r \) = Annual interest rate (10% or 0.10)
- \( n \) = Number of years (20)

Let's calculate the EAI.

\[
r = \frac{10}{100} = 0.10
\]

\[
n = 20
\]

\[
\text{EAI} = \frac{500000 \times 0.10 \times (1 + 0.10)^{20}}{(1 + 0.10)^{20} - 1}
\]

Now I'll compute the EAI.The equal annual installment (EAI) that S would need to pay is approximately ₹58,729.81.

Would you like further details or have any questions about the calculation?

Here are 5 related questions:
1. How does the interest rate affect the amount of the annual installment?
2. What would the installment be if the loan term were shorter, say 15 years?
3. How would a higher principal amount change the installment?
4. Can we calculate the total interest paid over the entire loan period?
5. How does the installment amount change if payments were monthly instead of annually?

**Tip:** Always double-check your interest rate and loan term when calculating installments, as even small changes can significantly impact the result.

Learn how to calculate the equal annual installment (EAI) for a ₹5,00,000 loan with 10% interest over a 20-year period. Understand the formula used and get a step-by-step solution. Suitable for advanced high school students studying finance and interest calculations.

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