Question

Jayanti lend Rs. 20,000 to Vinayak at 20% per annum compounded half-yearly. After a time period Vinayak returned Rs. 26,620 to Jayanti. Find the time period.
1. \(1{{3} \over 4}\) years
2. 2 years
3. \(1{{1} \over 2}\) years
4. 1 year

Answer 1

Correct Answer - Option 3 : \(1{{1} \over 2}\) years

Given:

Principal (P) = Rs.20,000

Amount (A) = Rs.26,620

Rate (R) = 20%

Condition = Halfyearly 

Concept used:

In halfyearly condition 

New time = 2 × Time 

New Rate == Rate/2

Formula used:

A = P(1 + R/100)n

Where,

A → amount

P → principal

R → rate 

n → time

Calculations:

Let the new time periods be n.

The rate of interest half-yearly = (20/2) = 10%

A = P(1 + R/100)n

⇒ 26620 = 20000(1 + 10/100)n

⇒ (11/10)n = 26620/20000

⇒ (11/10)n = 1331/1000

⇒ (11/10)n = (11/10)3

⇒ n = 3

New time = Time × 2

Thus time = (3/2) = \(1{{1} \over 2}\) years

∴ The time period is \(1{{1} \over 2}\) years.