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
1. Rs. 12,124
2. Rs. 12,143
3. Rs. 12,134
4. Rs. 12,314
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