Calculate Amount & CI on ₹30500 for 1½years at 8% per annum
compounded half yearly, with formula.
Answers
Step-by-step explanation:
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} }
✠Given
\sf \implies Principal \: (P) = Rs. \: 30500⟹Principal(P)=Rs.30500
\sf \implies Rate \: of \: interest = 8 \: \% = \dfrac{8}{2} = 4 \: \%⟹Rateofinterest=8%=
2
8
=4%
\sf \implies Time = 1 \: \dfrac{1}{2} \: years= \dfrac{3}{2} \: years \: = \dfrac{3}{2} \times 2 = 3 \: years.⟹Time=1
2
1
years=
2
3
years=
2
3
×2=3years.
\bf \underline{ \underline{\maltese\:To \: find } }
✠Tofind
\sf \implies Amount \: and \: compound \: interest = \: ?⟹Amountandcompoundinterest=?
\bf \underline{ \underline{\maltese\:Solution} }
✠Solution
\underline{\sf { \boxed{ { \sf \: Amount = Principal\: \bigg(\: 1 + \dfrac{Rate}{100} \: \bigg ) ^{Time} }}}}
Amount=Principal(1+
100
Rate
)
Time
\sf \implies {{ \sf \: Amount = 30500\: \bigg(\: 1 + \dfrac{4}{100} \: \bigg ) ^{3} }}⟹Amount=30500(1+
100
4
)
3
\sf \implies {{ \sf 30500\: \bigg(\: 1 + \dfrac{1}{25} \: \bigg ) ^{3} }}⟹30500(1+
25
1
)
3
\sf \implies {{ \sf 30500\: \bigg(\:\dfrac{25 + 1}{25} \: \bigg ) ^{3} }}⟹30500(
25
25+1
)
3
\sf \implies {{ \sf 30500\: \bigg(\: \dfrac{26}{25} \: \bigg ) ^{3} }}⟹30500(
25
26
)
3
\sf \implies \sf \cancel{30500} \times \dfrac{17576}{ \cancel{15625} }⟹
30500
×
15625
17576
\sf \implies \sf \dfrac{244 \times 17576}{125}⟹
125
244×17576
\sf \implies \sf \dfrac{4288544}{125} = 34308.352⟹
125
4288544
=34308.352
\sf \underline{ \boxed{ \sf Therefore, \: amount = Rs. \:34308.352 }}
Therefore,amount=Rs.34308.352
\bf \underline{Now},
Now
,
\sf Compound \: interest = Amount - PrincipalCompoundinterest=Amount−Principal
\sf \implies C.I = 34308.352 - 30500 = Rs. \: 3808.352⟹C.I=34308.352−30500=Rs.3808.352
\sf \underline{ \boxed{ \sf Hence, Compound \: interest = Rs. \: 3808.352 }}
Hence,Compoundinterest=Rs.3808.352
━━━━━━━━━━━━━━━━━━━━━━━━━━
Solution : 3
\bf \underline{ \underline{\maltese\:Given} }
✠Given
\sf \implies Principal \: (P) = Rs. \:18000⟹Principal(P)=Rs.18000
\sf \implies Rate \: of \: interest = 9\: \%⟹Rateofinterest=9%
\sf \implies Time = 3 \: years⟹Time=3years
\bf \underline{ \underline{\maltese\:To \: find } }
✠Tofind
\sf Difference \: between \: compound \: interest \: and \: simple \: Interest = \: ?DifferencebetweencompoundinterestandsimpleInterest=?
\bf \underline{ \underline{\maltese\:Solution } }
✠Solution
\sf Finding \: the \: simple \: interest,Findingthesimpleinterest,
\underline{\boxed{ \sf Simple \: interest = \dfrac{Principal \times Rate \times Time}{100} }}
Simpleinterest=
100
Principal×Rate×Time
\sf \implies Simple \: interest = \cancel{\dfrac{18000 \times 9 \times 3}{100} } = 4860⟹Simpleinterest=
100
18000×9×3
=4860
\sf \underline{Hence, \: simple \: interest = Rs. \: 4860 }
Hence,simpleinterest=Rs.4860
\sf Now, \: finding \: the \: compound \: interest,Now,findingthecompoundinterest,
\underline{\sf { \boxed{ { \sf \: Amount = Principal\: \bigg(\: 1 + \dfrac{Rate}{100} \: \bigg ) ^{Time} }}}}
Amount=Principal(1+
100
Rate
)
Time
\sf \implies {{ \sf \: Amount = 18000\: \bigg(\: 1 + \dfrac{9}{100} \: \bigg ) ^{3} }}⟹Amount=18000(1+
100
9
)
3
\sf \implies {{ \sf \: 18000\: \bigg(\: \dfrac{100 + 9}{100} \: \bigg ) ^{3} }}⟹18000(
100
100+9
)
3
\sf \implies {{ \sf \: 18000\: \bigg(\: \dfrac{109}{100} \: \bigg ) ^{3} }}⟹18000(
100
109
)
3
\sf \implies {{ \sf \: \cancel{18000} \times \dfrac{1295029}{ \cancel{1000000} }}}⟹
18000
×
1000000
1295029
\sf \implies {{ \sf \dfrac{9 \times 1295029}{ 500 }}}⟹
500
9×1295029
\sf \implies {{ \sf \dfrac{11655261}{ 500 }}} = 23310.522⟹
500
11655261
=23310.522
\sf \boxed{ \sf Therefore, \: amount = Rs. \:23310.522 }
Therefore,amount=Rs.23310.522
\sf Compound \: interest = Amount - PrincipalCompoundinterest=Amount−Principal
\sf \implies C.I = 23310.522 - 18000 = Rs. \: 5310.522⟹C.I=23310.522−18000=Rs.5310.522
\sf \boxed{ \sf Hence, Compound \: interest = Rs. \: 5310.522 }
Hence,Compoundinterest=Rs.5310.522
\bf \underline{ Now},
Now
,
\sf Difference = Compound \: interest - Simple \: InterestDifference=Compoundinterest−SimpleInterest
\sf \implies 5310.522 - 4860 = 450.522⟹5310.522−4860=450.522
\sf \underline{ \boxed{ \sf Therefore, \: difference \: between\: C.I \: and \: S.I = Rs. \: 450.522 }} \:
Therefore,differencebetweenC.IandS.I=Rs.450.522