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(A) Principal $(P)$ = ₹ $5000$,Rate $(R)$ = $4 \%$ per annum,Time $(n)$ = $1 \frac{1}{2}$ years = $3$ half-years.Case $1$: Compounded yearly.For the f

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$2.04$

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(A) Principal $(P)$ = ₹ $5000$,Rate $(R)$ = $4 \%$ per annum,Time $(n)$ = $1 \frac{1}{2}$ years = $3$ half-years.Case $1$: Compounded yearly.For the first year,interest is calculated yearly. For the remaining half-year,simple interest is applied.Amount $= 5000 	imes (1 + \frac{4}{100})^1 	imes (1 + \frac{2}{100})^1 = 5000 	imes \frac{26}{25} 	imes \frac{51}{50} = 200 	imes 26 	imes \frac{51}{50} = 4 	imes 26 	imes 51 = ₹ 5304$.Compound Interest $(CI_1)$ $= 5304 - 5000 = ₹ 304$.Case $2$: Compounded half-yearly.Rate $(r)$ = $4/2 = 2 \%$ per half-year,Time $(n)$ = $3$ half-years.Amount $= 5000 	imes (1 + \frac{2}{100})^3 = 5000 	imes (1.02)^3 = 5000 	imes 1.061208 = ₹ 5306.04$.Compound Interest $(CI_2)$ $= 5306.04 - 5000 = ₹ 306.04$.Difference $= CI_2 - CI_1 = 306.04 - 304 = ₹ 2.04$.

What is the difference between the compound interests (in ₹) on ₹ $5000$ for $1 \frac{1}{2}$ years at $4 \%$ per annum compounded yearly and half-yearly?

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