A sum of Rs 2500 is invested at 10% per annum Compounded annually and half yearly for a period of 1 year. Find the difference between the interest ear

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A sum of Rs 2500 is invested at 10% per annum Compounded annually and half yearly for a period of 1 year. Find the difference between the interest earned in both the cases.
1. Rs 6.25
2. Rs 7
3. Rs 6.85
4. Rs 9

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Correct Answer - Option 1 : Rs 6.25

Given:

Principal = Rs 2500

Rate = 10% per annum

Time = 1 Year

Formula Used:

${\rm{A}} = P{\left[ {1 + \frac{r}{{100}}} \right]^n}$

Compound interest = Amount - Principal

Concept Used:

If Rate is compounded half yearly, then we half the rate given

If it is compounded half yearly then we have two terms of 6 months so we take n as 2

Calculation:

For the rate to be compounded annually,

Amount = ${\rm{A}} = 2500{\left[ {1 + \frac{{10}}{{100}}} \right]^1}$

⇒ A = (2500 × 11)/10

⇒ A = Rs 2750

Compound interest = 2750 - 2500 = Rs 250

For the interest to be compounded half yearly,

Amount = ${\rm{A}} = 2500{\left[ {1 + \frac{5}{{100}}} \right]^2}$

⇒ A = (2500 × 21 × 21)/(20 × 20) = Rs 2756.25

Compound Interest = 2756.25 - 2500 = Rs 256.25

Difference between two compound interest = 256.25 - 250 = Rs 6.25

∴ The difference between the interest earned in both the cases will be Rs 6.25