Question

The difference in compound interest on a certain sum at 20% p.a. for one year, when the interest is compounded half-yearly and yearly, is Rs 757.8 then, what is the simple interest on the same sum for 1.5 years at the same rate?

 

1. Rs 22734
2. Rs 23466
3. Rs 22675
4. Rs 23425

Answer 1

Correct Answer - Option 1 : Rs 22734

Given:

Rate = 20%

Formula used:

SI = (P × R × T)/100

For CI,

Amount = P(1 + r/100)n

Amount = P + CI

Here n is the time

Concept used:

In case of half yearly, the rate is half and time is doubled

CI and SI is same for first year

Calculation:

Let the sum be x

CI for half yearly

Rate = 20%/2 = 10%

Amount = P(1 + r/100)n

⇒ x(1 + 10/100)2

⇒ 121x/100

CI = 121x/100 – x = 21x/100

And for yearly,

SI = CI = (x × 20 × 1)/100

⇒ 20x/100

Now, A/Q,

21x/100 – 20x/100 = 757.8

⇒ x = 75780

Now, SI = (75780 × 20 × 1.5)/100 = 22734

∴ The required simple interest is Rs 22734