A sum of Rs. 10,500 amounts to Rs. 13,650 in 2 years at a certain rat

1.	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. 12,1242. Rs. 12,1433. Rs. 12,1344. Rs. 12,314
Answer» 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

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. 12,1242. Rs. 12,1433. Rs. 12,1344. Rs. 12,314

Answer» 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