Question

A sum of Rs. 10,500 amounts to Rs. 13,650 in 2 years at a certain rate percent per annum simple interest. The same sum will amount to what in 1 year at the same rate, if the interest is compounded half yearly (nearest to Rs.1)?
1. Rs. 12,124
2. Rs. 12,143
3. Rs. 12,134
4. Rs. 12,314

Answer 1

Correct Answer - Option 3 : Rs. 12,134

Given :-

A sum of Rs. 10,500 amounts to Rs. 13,650 in 2 years at a certain rate percent per annum simple interest

compounded half yearly

Concept :-

Simple interest = (Principal × rate × time)/100

Simple interest = Amount - Principal

Compound interest = Amount - Principal 

Amount = Principal(1 + (r/100))^t

If interest is compounded half yearly then time become double and rate become half

Calculation :-

⇒ Simple interest = 13,650 - 10,500

⇒ Simple interest = Rs. 3150

⇒ 3150 = (10,500 × r × 2)/100

⇒ 3150 = 105 × r × 2

⇒ r = 3150/(105 × 2)

⇒ r = 15%

Now,

For compounded half yearly

⇒ Rate = (15/2)%

⇒ Time = 2 years

⇒ Amount = 10,500(1 + (15/200))²

⇒ Amount = 10,500(1 + (3/40))²

⇒ Amount = 10,500 × (43/40) × (43/40)

⇒ Amount = 12,134

∴ The sum will amount is 12,134