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