find the amount to be paid at the end of third year if principal amount is rupees10000 and Rate of interest is 11 percentage.
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Answer:
Here, Principal (P) = Rs. 10000, Rate of Interest (R) = 10% = 5% (compounded half yearly)
Time(n) = 1\ \frac{1}{2}1
2
1
years = 3 years (compounded half yearly)
Amount (A) = P\left(1+\frac{R}{100}\right)^nP(1+
100
R
)
n
= 10000\left(1+\frac{5}{100}\right)^310000(1+
100
5
)
3
= 10000\left(1+\frac{1}{20}\right)^310000(1+
20
1
)
3
= 10000\left(\frac{21}{20}\right)^310000(
20
21
)
3
= 10000\times\frac{21}{20}\times\frac{21}{20}\times\frac{21}{20}10000×
20
21
×
20
21
×
20
21
= Rs. 11,576.25
Compound Interest (C.I.) = A – P
= Rs. 11,576.25 – Rs. 10,000 = Rs. 1,576.25
If it is compounded annually, then
Here, Principal (P) = Rs. 10000, Rate of Interest (R) = 10%, Time (n) = 1\ \frac{1}{2}1
2
1
years.
Amount (A) for 1 year = P\left(1+\frac{R}{100}\right)^nP(1+
100
R
)
n
= 10000\left(1+\frac{10}{100}\right)^110000(1+
100
10
)
1
= 10000\left(1+\frac{1}{10}\right)^110000(1+
10
1
)
1
= 10000\left(\frac{11}{10}\right)^110000(
10
11
)
1
= 10000\times\frac{11}{10}10000×
10
11
= Rs. 11,000
Interest for \frac{1}{2}
2
1
year = \frac{11000\times1\times10}{2\times100}=RS.\ 550
2×100
11000×1×10
=RS. 550
\therefore∴ Total amount = Rs. 11,000 + Rs. 550 = Rs. 11,550
Now, C.I. = A – P = Rs. 11,550 – Rs. 10,000
= Rs. 1,550
Yes, interest Rs. 1,576.25 is more than Rs. 1,550.
Step-by-step explanation:
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