Question

Shantanu borrows ₹ 65000 from a bank at 10% per annum compounded yearly. He repays ₹ 21500 at the end of first year and ₹ 25000 at the end of second year. Find the remaining amount at the beginning of third year.

Answer 1

Given:

• Principal (P) = ₹ 65000
• Rate of interest (R) = 10% per annum compounded yearly
• Repayment at end of 1st year = ₹ 21500
• Repayment at end of 2nd year = ₹ 25000
• Find remaining amount at the beginning of the 3rd year

Stepwise calculation:

1. Calculate amount at the end of 1st year before repayment:

Amount after 1 year with compound interest:

`A_1 = P xx (1 + R/100)^1`

A₁ = 65000 × 1.10

A₁ = ₹ 71500

2. Subtract the repayment at the end of 1st year:

Remaining principal after 1st year repayment:

P₁ = A₁ – 21500

P₁ = 71500 – 21500

P₁ = ₹ 50000

3. Calculate amount at the end of 2nd year before repayment (on the remaining principal after 1st repayment):

`A_2 = P_1 xx (1 + R/100)^1`

A₂ = 50000 × 1.10

A₂ = 55000

4. Subtract the repayment at the end of 2nd year:

Remaining principal after 2nd year repayment:

P₂ = A₂ – 25000

P₂ = 55000 – 25000

P₂ = ₹ 30000

5. Remaining amount at the beginning of 3rd year is ₹ 30000.