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In what time will Rs. 6,250 amount to Rs. 6,632.55 at 4% compound interest payable half-yearly?
1. 1 year
2. \(\frac{3}{2}\)years
3. 3years
4. \(\frac{5}{2}\)years

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

Concept Used:

For half yearly, rate is halved and time period gets doubled.

Formula Used:

Amount = P × (1 + r/100)t

where, P → Principal, r → Rate of interest, t → Time period

Calculations:

Let the time period be t years.

Principal = Rs. 6250

Amount after compound interest = Rs. 6632.55

Rate of interest = 4%

For half-yearly,

⇒ 6632.55 = 6250 × (1 + (4/2)/100)2t

⇒ (6632.55/6250) = (51/50)2t

⇒ (132651/12500) = (51/50)2t

⇒ (51/50)= (51/50)2t

On comparing both, we get

2t = 3

⇒ t = 3/2 years

∴ The required time is 3/2 years.

When a sum is invested at half-yearly, then time gets doubled, so actual time for which money is invested is 3/2 years instead of 3 years.

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