Rs.1000 is invested at 5% per annum simple interest. If the interest is added to the principal after every 10 years, the amount will become Rs. 2,000 after

Given:

Principal (P) = Rs. 1,000

Rate of Interest (R) = 5% per annum

Interest is added to the principal every 10 years

Final Amount (A) = Rs. 2,000

Formula Used:

Simple Interest (SI) = P × R × T / 100

Calculation:

For the first 10 years:

SI₁ = 1000 × 5 × 10 / 100

SI₁ = 500

Amount after 10 years = Principal + SI₁

Amount₁ = 1000 + 500

Amount₁ = 1500

For the next 10 years:

Principal for the next 10 years = Amount₁

SI₂ = 1500 × 5 × 10 / 100

SI₂ = 750

Amount after 20 years = Principal + SI₂

Amount₂ = 1500 + 750

Amount₂ = 2250

Since Amount₂ (Rs. 2250) exceeds Rs. 2000, we need to find the exact time when it becomes Rs. 2000.

Let the time required after the first 10 years be T years to reach Rs. 2000:

SI = 1500 × 5 × T / 100

Interest needed = 2000 - 1500 = 500

⇒ 1500 × 5 × T / 100 = 500

⇒ 75T = 500

⇒ T = 500 / 75

⇒ T = 6 (2/3) years

Total time = 10 + 6 (2/3) years

Total time = 16 (2/3) years

Therefore, the correct answer is option 4: 16 (2/3) years.