Find the compound interest for Rs. 6000 at 4% rate, compounded annually, for 2 years.
Answers
Answer:
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Step-by-step explanation:
Given:-
Principal = Rs.6000
Rate of interest = 4% p.a.
Time = 1 year
To Find:-
Compound interest, if the interest is compounded half-yearly
Compound interest, if the interest is compounded quarterly.
Solution:-
Firstly as we are given with the values of:-
Principal = Rs.6000
Rate = 4% p.a.
Time = 1
i) Let us find the compounded interest is the sum is compounded half-yearly.
We know,
\sf{A = P\bigg(1+\dfrac{r}{200}\bigg)^{2n}}A=P(1+
200
r
)
2n
Hence,
\sf{A = 6000\bigg(1+\dfrac{4}{200}\bigg)^{2\times 1}}A=6000(1+
200
4
)
2×1
= \sf{A = 6000\bigg(1+\dfrac{1}{50}\bigg)^2}A=6000(1+
50
1
)
2
= \sf{A = 6000\bigg(\dfrac{50+1}{50}\bigg)^2}A=6000(
50
50+1
)
2
= \sf{A = 6000\times \dfrac{51}{50}\times \dfrac{51}{50}}A=6000×
50
51
×
50
51
= \sf{A = 6242.4}A=6242.4
Now,
CI = Amount - Principal
= CI = 6242.2 - 6000
= CI = 242.2
Therefore, CI after 1 year if the interest is compounded half-yearly will be Rs.242.2.
______________________________________
ii) Let us find the compound interest after 1 year if the interest is compounded quarterly.
We know,
\sf{A = P\bigg(1+\dfrac{r}{400}\bigg)^{4n}}A=P(1+
400
r
)
4n
Hence,
\sf{A = 6000\bigg(1+\dfrac{4}{400}\bigg)^{4\times1}}A=6000(1+
400
4
)
4×1
= \sf{A = 6000\bigg(1+\dfrac{1}{100}\bigg)^4}A=6000(1+
100
1
)
4
= \sf{A = 6000\bigg(\dfrac{100+1}{100}\bigg)^4}A=6000(
100
100+1
)
4
= \sf{A = 6000\bigg(\dfrac{101}{100}\bigg)^4}A=6000(
100
101
)
4
= \sf{A = 6000\times \dfrac{101}{100}\bigg)\times \bigg(\dfrac{101}{100}\bigg)\times \bigg(\dfrac{101}{100}\bigg)}A=6000×
100
101
)×(
100
101
)×(
100
101
)
= \sf{A = \dfrac{624362406000}{100000000}}A=
100000000
624362406000
= \sf{A = 6243.62406}A=6243.62406
=> \sf{A = Rs.6243.6}A=Rs.6243.6
Now,
CI = A - P
= CI = 6243.6 - 6000
= CI = 243.6
Therefore, CI after 1 year if the interest is compounded annually will be Rs.243.6
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