The sum of Rs. 3200 invested at 10% per annum compounded quarterly amo

1.	The sum of Rs. 3200 invested at 10% per annum compounded quarterly amounts to Rs. 3362, then find the time period.1. ½ year2. ¼ year3. ¾ year4. 1 year
Answer» Correct Answer - Option 1 : ½ year Given: Principal = Rs 3200 Rate of interest = 10% per annum Amount = Rs 3362 Concept used: Amount = P × [1 + (r/100)]^t But here, the amount is calculated quarterly. Then the amount obtained will be: Amount = P × [1 + r/(n × 100)]^nt Where n is the number of terms, here n = 4. Calculation: 3362 = 3200 × [1 + 10/(4 × 100]^4t ⇒ 3362/3200 = (41/40)^4t ⇒ 1681/1600 = (41/40)4t ⇒ (41/40)² = (41/40)^4t On comparing powers, ⇒ 2 = 4t ⇒ t = 1/2 ∴ The time period is 1/2 year.

The sum of Rs. 3200 invested at 10% per annum compounded quarterly amounts to Rs. 3362, then find the time period.1. ½ year2. ¼ year3. ¾ year4. 1 year

Answer» Correct Answer - Option 1 : ½ year

Given:

Principal = Rs 3200

Rate of interest = 10% per annum

Amount = Rs 3362

Concept used:

Amount = P × [1 + (r/100)]^t

But here, the amount is calculated quarterly. Then the amount obtained will be:

Amount = P × [1 + r/(n × 100)]^nt

Where n is the number of terms, here n = 4.

Calculation:

3362 = 3200 × [1 + 10/(4 × 100]^4t

⇒ 3362/3200 = (41/40)^4t

⇒ 1681/1600 = (41/40)4t

⇒ (41/40)² = (41/40)^4t

On comparing powers,

⇒ 2 = 4t

⇒ t = 1/2

∴ The time period is 1/2 year.

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