Question

Bhumica lend Rs. 6,000 to Shivam at 10% per annum compounded half-yearly. After a time period Shivam returned Rs. 6,615 to Bhumica. Find the time period.

1. 1 year
2. 2 year
3. (1/2) year
4. 3 year

Answer 1

Correct Answer - Option 1 : 1 year

Given:

Principal (P) = Rs.6,000

Amount (A) = Rs.6,615

Rate (R) = 10%

Condition = Half yearly

Concept used:

When the condition is Halfyearly

So, New time = Initial time × 2

New rate = (Initial Rate)/2

Formula used:

A = P(1 + R/100)n

Where

A → Amount

P → Principal

R → Rate 

n → Time

Calculations:

Let the number of new time periods be n.

The rate of interest half-yearly = (10/2) = 5%

A = P(1 + R/100)n

⇒ 6615 = 6000(1 + 5/100)n

⇒ (21/20)n = 6615/6000

⇒ (21/20)n = 441/400

⇒ (21/20)n = (21/20)2

⇒ n = 2

So,initial time period = (2/2) = 1 year

∴ The time period is 1 year.