https://file.aiquickdraw.com/mathbot/file/1727428837169zxqjkwx0.jpg

Find the  total  number of installments  he has to pay

Let's break down the question based on the provided image.

The question states that:
- Your father wants to buy a flat and plans to take a loan from a bank.
- The total loan amount is **Rs. 15,39,000**.
- He will repay the loan in installments, starting with **Rs. 13,000** in the first month.
- He increases the installment by **Rs. 1,300** every month.

This forms an **arithmetic progression (AP)** where:
- The first installment \( a_1 = Rs. 13,000 \),
- The common difference \( d = Rs. 1,300 \),
- The total loan amount \( S = Rs. 15,39,000 \).

In an arithmetic progression, the sum of \( n \) terms is given by:

\[
S_n = \frac{n}{2} [2a_1 + (n-1)d]
\]

Where:
- \( n \) is the number of terms (installments),
- \( S_n \) is the total sum (loan amount),
- \( a_1 \) is the first term (installment),
- \( d \) is the common difference.

We need to find \( n \), the number of installments. Let's solve for \( n \) using the values provided.

\[
S_n = \frac{n}{2} [2 \times 13000 + (n - 1) \times 1300]
\]
\[
1539000 = \frac{n}{2} [26000 + 1300(n - 1)]
\]

Now I'll calculate the value of \( n \).The values of \( n \) (the number of installments) obtained include negative solutions, which are not physically meaningful for this context. Therefore, only the positive solution is valid. After calculation, the total number of installments turns out to be approximately **22.66**.

Since the number of installments must be a whole number, he will need to pay **23 installments** to fully repay the loan.

Would you like more details or have any other questions?

Here are some related questions:
1. How would the total change if the initial installment was different?
2. What is the total amount paid by the last installment?
3. How does increasing the monthly installment affect the total number of payments?
4. What if the increase per month was Rs. 1,000 instead of Rs. 1,300?
5. How can you calculate the loan if the bank has interest?

**Tip:** The formula for an arithmetic progression can also be used to calculate cumulative payments over time.

Your father wants to buy a flat and plans to take a loan from a bank. He repays his total loan of Rs. 15,39,000 by paying an installment of Rs. 13,000 every month, starting with the first installment of Rs. 13,000. Also, he increases the installment by Rs. 1,300 every month. Find the total number of installments he has to pay.

Learn how to calculate the total number of installments required to repay a loan of Rs. 15,39,000 with monthly installments starting at Rs. 13,000 and increasing by Rs. 1,300 every month. This problem uses arithmetic progression concepts, making it ideal for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation