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Calculate the amount and compound interest on:
(a) ₹10,800 for 3 years at 12 1/2% per annum compounded half annually..
(b) ₹18, 000 for 2 1/2 years at 10% per annum compounded annually.
Answers
Answer:
Solution:
(a) Here, Principal (P) = Rs. 10800, Time (n) = 3 years Rate of interest (R) = 12\ \frac{1}{2}\%=\frac{25}{2\%}
Amount(A) = P\left(1+\frac{R}{100}\right)^n
= 10800\left(1+\frac{1}{8}\right)^3=10800\left(\frac{9}{8}\right)^3
= 10800\times\frac{9}{8}\times\frac{9}{8}\times\frac{9}{8}
= Rs. 15,377.34
Compound Interest (C.I.) = A – P
= Rs. 10800 – Rs. 15377.34 = Rs. 4,577.34
(b) Here, Principal (P) = Rs. 18,000, Time (n) = 2\ \frac{1}{2} years, Rate of interest (R) = 10% p.a.
Amount(A) = P\left(1+\frac{R}{100}\right)^n
= 18000\left(1+\frac{10}{100}\right)^2=18000\left(1+\frac{1}{10}\right)^2
= 18000\left(\frac{11}{10}\right)^2=18000\times\frac{11}{10}\times\frac{11}{10}
= Rs. 21,780
Interest for \frac{1}{2} years on Rs. 21,780 at rate of 10% = \frac{21780\times10\times1}{100}= Rs. 1089
Total amount for 2\ \frac{1}{2} years.
= Rs. 21,780 + Rs. 1089 = Rs. 22,869
Compound Interest (C.I.) = A – P
= Rs. 22869 – Rs. 18000 = Rs. 4,869
(c) Here, Principal (P) = Rs. 62500, Time (n) = 1\ \frac{1}{2}=\frac{3}{2} years = 3 years
Rate of interest (R) = 8% = 4% (compounded half yearly)
Amount (A) = P\left(1+\frac{R}{100}\right)^n
= 62500\left(1+\frac{4}{100}\right)^2
= 62500\left(1+\frac{1}{25}\right)^3
= 62500\left(\frac{26}{25}\right)^3
= 62500 \times\frac{26}{25}\times\frac{26}{25}\times\frac{26}{25}
= Rs. 70,304
Compound Interest (C.I.) = A – P
= Rs. 70304 – Rs. 62500 = Rs. 7,804
(d) Here, Principal (P) = Rs. 8000, Time (n) = 1 years = 2 years (compounded half yearly)
Rate of interest (R) = 9% = \frac{9}{2}\% (compounded half yearly)
Amount (A) = P\left(1+\frac{R}{100}\right)^n
= 8000\left(1+\frac{9}{2\times100}\right)^2
= 8000\left(1+\frac{9}{200}\right)^2
= 800\left(\frac{209}{200}\right)^2
= 8000\times\frac{209}{200}\times\frac{209}{200}
= Rs. 8,736.20
Compound Interest (C.I.) = A – P
= Rs. 8736.20 – Rs. 8000
= Rs. 736.20
(e) Here, Principal (P) = Rs. 10,000, Time (n) = 1 years = 2 years (compounded half yearly)
Rate of interest (R) = 8% = 4% (compounded half yearly)
Amount (A) = P\left(1+\frac{R}{100}\right)^n
= 10000\left(1+\frac{4}{100}\right)^2
= 10000\left(1+\frac{1}{25}\right)^2
= 10000\left(\frac{26}{25}\right)^2
= 10000\times\frac{26}{25}\times\frac{26}{25}
= Rs. 10,816
Compound Interest (C.I.) = A – P
= Rs. 10,816 – Rs. 10,000 = Rs. 816
Calculate Amount and Compound Interest
Here, P=10,800
n=3 years
12=12
2
1
%=
2
25
%
A=P(1+
100
R
)
n
=10,800(1+
100
25
)
3
=10,800(
200
225
)
3
=10,800×
200
225
×
200
225
×
200
225
A=15377.34Rs
Compound Interest=Amount-P
=15377.34−10,800
=4577.34Rs