6. Find the amount and the compound interest on 1,600 for three years if the rates for three yea
are 4%, 5% and 8%, respectively, the interest being payable annually.
Answers
Given that
We know,
☆ If a certain sum of money P is invested for successive rate of interest, then amount A is given by
☆ On substituting the values, we get
Hence,
We know,
Hence,
Additional Information :-
☆ If a certain sum of money Rs P is invested at the rate of r % per annum compounded annually for the time period of n years, then Amount is
☆ If a certain sum of money Rs P is invested at the rate of r % per annum compounded half yearly for the time period of n years, then Amount is
☆ If a certain sum of money Rs P is invested at the rate of r % per annum compounded quarterly for the time period of n years, then Amount is
Answer:
Solution−
Given that
\: \: \: \: \: \bull \: \: \: \sf{ Sum\:_{(money)}=Rs \: 1600}∙Sum
(money)
=Rs1600
\: \: \: \: \: \bull \: \: \:\sf{ Rate \: of \: interest\:_{(r_1)}=4\%}∙Rateofinterest
(r
1
)
=4%
\: \: \: \: \: \bull \: \: \:\sf{ Time\:_{(t_1)}=1\: year}∙Time
(t
1
)
=1year
\: \: \: \: \: \bull \: \: \:\sf{ Rate \: of \: interest\:_{(r_2)}=5\%}∙Rateofinterest
(r
2
)
=5%
\: \: \: \: \: \bull \: \: \:\sf{ Time\:_{(t_2)}=1\: year}∙Time
(t
2
)
=1year
\: \: \: \: \: \bull \: \: \:\sf{ Rate \: of \: interest\:_{(r_3)}=8\%}∙Rateofinterest
(r
3
)
=8%
\: \: \: \: \: \bull \: \: \:\sf{ Time\:_{(t_3)}=1\: year}∙Time
(t
3
)
=1year
We know,
☆ If a certain sum of money P is invested for successive rate of interest, then amount A is given by
\rm :\longmapsto\:A = P {\bigg(1 + \dfrac{r_1}{100} \bigg) }^{t_1}{\bigg(1 + \dfrac{r_2}{100} \bigg) }^{t_2}{\bigg(1 + \dfrac{r_3}{100} \bigg) }^{t_3}:⟼A=P(1+
100
r
1
)
t
1
(1+
100
r
2
)
t
2
(1+
100
r
3
)
t
3
☆ On substituting the values, we get
\rm :\longmapsto\:A = 1600{\bigg(1 + \dfrac{4}{100}\bigg) }^{1}{\bigg(1 + \dfrac{5}{100}\bigg) }^{1}{\bigg(1 + \dfrac{8}{100}\bigg) }^{1}:⟼A=1600(1+
100
4
)
1
(1+
100
5
)
1
(1+
100
8
)
1
\rm :\longmapsto\:A = 1600 \times (1.04) \times (1.05) \times (1.08):⟼A=1600×(1.04)×(1.05)×(1.08)
\rm :\longmapsto\:A = 1886.98:⟼A=1886.98
Hence,
\: \: \: \: \red{ \boxed{ \bf{ \: Amount \: after \: 3 \: years = Rs \: 1886.98}}}
Amountafter3years=Rs1886.98
We know,
\red{\rm :\longmapsto\:Compound \: Interest = Amount - Principal}:⟼CompoundInterest=Amount−Principal
\: \: \rm \: = \: \:1886.98 - 1600=1886.98−1600
\: \: \rm \: = \: \:286.98=286.98
Hence,
\red{ \boxed{ \bf{ \: Compound \: Interest \: after \: 3 \: years = Rs \: 286.98}}}
CompoundInterestafter3years=Rs286.98
Additional Information :-
☆ If a certain sum of money Rs P is invested at the rate of r % per annum compounded annually for the time period of n years, then Amount is
\boxed{ \sf \: A = P{\bigg(1 + \dfrac{r}{100} \bigg) }^{n}}
A=P(1+
100
r
)
n
☆ If a certain sum of money Rs P is invested at the rate of r % per annum compounded half yearly for the time period of n years, then Amount is
\boxed{ \sf \: A = P{\bigg(1 + \dfrac{r}{200} \bigg) }^{2n}}
A=P(1+
200
r
)
2n
☆ If a certain sum of money Rs P is invested at the rate of r % per annum compounded quarterly for the time period of n years, then Amount is
\boxed{ \sf \: A = P{\bigg(1 + \dfrac{r}{400} \bigg) }^{4n}}
A=P(1+
400
r
)
4n