Question

Amrit Raj borrows ₹ 50,000 from a bank at 9% p.a. compound interest. He repays ₹ 24,500 at the end of first year and ₹ 12,700 at the end of the second year. Find the amount outstanding at the beginning of the third year.

Answer 1

Given:

• Principal P = ₹ 50,000 
• Rate r = 9% p.a, compounded annually
• Repayments: ₹ 24,500 after 1 year, ₹ 12,700 after 2 years

Step 1: Amount at the end of the first year

`A_1 = P(1 + r/100)`

A₁ = 50,000 × 1.09

A₁ = 54,500

Rahul repays ₹ 24,500 at the end of first year:

Outstanding after 1st year = 54,500 − 24,500 = 30,000

Step 2: Amount at the end of the second year

Now the new principal = ₹ 30,000

A₂ = 30,000 × 1.09

A₂ = 32,700

Rahul repays ₹ 12,700 at the end of the second year:

Outstanding after 2nd year = 32,700 − 12,700 = 20,000

Step 3: Amount outstanding at the beginning of 3rd year 

The principal for the 3rd year = Outstanding after 2nd year = ₹ 20,000