Question

● Sum 2: Calculate Amount & CI on ₹30500 for 1½years at 8% per annum

compounded half yearly, with formula.

● Sum 3: Calculate SI & CI on ₹18000 for 3 years at 9% per annum, with formula.

Also find the difference between Simple Interest and Compound Interest.
DO NOT SPAM​

Answer 1

Solution : 2

⟶ Note : When interest is compounded half yearly, then rate of interest would be halfed and time (n) will be doubled that is 2n.

$\bf \underline{ \underline{\maltese\:Given} }$

$\sf \implies Principal \: (P) = Rs. \: 30500$

$\sf \implies Rate \: of \: interest = 8 \: \% = \dfrac{8}{2} = 4 \: \%$

$\sf \implies Time = 1 \: \dfrac{1}{2} \: years= \dfrac{3}{2} \: years \: = \dfrac{3}{2} \times 2 = 3 \: years.$

$\bf \underline{ \underline{\maltese\:To \: find } }$

$\sf \implies Amount \: and \: compound \: interest = \: ?$

$\bf \underline{ \underline{\maltese\:Solution} }$

$\underline{\sf { \boxed{ { \sf \: Amount = Principal\: \bigg(\: 1 + \dfrac{Rate}{100} \: \bigg ) ^{Time} }}}}$

$\sf \implies {{ \sf \: Amount = 30500\: \bigg(\: 1 + \dfrac{4}{100} \: \bigg ) ^{3} }}$

$\sf \implies {{ \sf 30500\: \bigg(\: 1 + \dfrac{1}{25} \: \bigg ) ^{3} }}$

$\sf \implies {{ \sf 30500\: \bigg(\:\dfrac{25 + 1}{25} \: \bigg ) ^{3} }}$

$\sf \implies {{ \sf 30500\: \bigg(\: \dfrac{26}{25} \: \bigg ) ^{3} }}$

$\sf \implies \sf \cancel{30500} \times \dfrac{17576}{ \cancel{15625} }$

$\sf \implies \sf \dfrac{244 \times 17576}{125}$

$\sf \implies \sf \dfrac{4288544}{125} = 34308.352$

$\sf \underline{ \boxed{ \sf Therefore, \: amount = Rs. \:34308.352 }}$

$\bf \underline{Now},$

$\sf Compound \: interest = Amount - Principal$

$\sf \implies C.I = 34308.352 - 30500 = Rs. \: 3808.352$

$\sf \underline{ \boxed{ \sf Hence, Compound \: interest = Rs. \: 3808.352 }}$

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Solution : 3

$\bf \underline{ \underline{\maltese\:Given} }$

$\sf \implies Principal \: (P) = Rs. \:18000$

$\sf \implies Rate \: of \: interest = 9\: \%$

$\sf \implies Time = 3 \: years$

$\bf \underline{ \underline{\maltese\:To \: find } }$

$\sf Difference \: between \: compound \: interest \: and \: simple \: Interest = \: ?$

$\bf \underline{ \underline{\maltese\:Solution } }$

$\sf Finding \: the \: simple \: interest,$

$\underline{\boxed{ \sf Simple \: interest = \dfrac{Principal \times Rate \times Time}{100} }}$

$\sf \implies Simple \: interest = \cancel{\dfrac{18000 \times 9 \times 3}{100} } = 4860$

$\sf \underline{Hence, \: simple \: interest = Rs. \: 4860 }$

$\sf Now, \: finding \: the \: compound \: interest,$

$\underline{\sf { \boxed{ { \sf \: Amount = Principal\: \bigg(\: 1 + \dfrac{Rate}{100} \: \bigg ) ^{Time} }}}}$

$\sf \implies {{ \sf \: Amount = 18000\: \bigg(\: 1 + \dfrac{9}{100} \: \bigg ) ^{3} }}$

$\sf \implies {{ \sf \: 18000\: \bigg(\: \dfrac{100 + 9}{100} \: \bigg ) ^{3} }}$

$\sf \implies {{ \sf \: 18000\: \bigg(\: \dfrac{109}{100} \: \bigg ) ^{3} }}$

$\sf \implies {{ \sf \: \cancel{18000} \times \dfrac{1295029}{ \cancel{1000000} }}}$

$\sf \implies {{ \sf \dfrac{9 \times 1295029}{ 500 }}}$

$\sf \implies {{ \sf \dfrac{11655261}{ 500 }}} = 23310.522$

$\sf \boxed{ \sf Therefore, \: amount = Rs. \:23310.522 }$

$\sf Compound \: interest = Amount - Principal$

$\sf \implies C.I = 23310.522 - 18000 = Rs. \: 5310.522$

$\sf \boxed{ \sf Hence, Compound \: interest = Rs. \: 5310.522 }$

$\bf \underline{ Now},$

$\sf Difference = Compound \: interest - Simple \: Interest$

$\sf \implies 5310.522 - 4860 = 450.522$

$\sf \underline{ \boxed{ \sf Therefore, \: difference \: between\: C.I \: and \: S.I = Rs. \: 450.522 }} \:$