calculate the amount and compound interest on Rs.18,000 for 2 1/2 years at 10% per annum compounded annually
Answers
Answer:
(a) Here, Principal (P) = Rs. 10800, Time (n) = 3 years Rate of interest (R) = 12\ \frac{1}{2}\%=\frac{25}{2\%}12
2
1
%=
2%
25
Amount(A) = P\left(1+\frac{R}{100}\right)^nP(1+
100
R
)
n
= 10800\left(1+\frac{1}{8}\right)^3=10800\left(\frac{9}{8}\right)^3(1+
8
1
)
3
=10800(
8
9
)
3
= 10800\times\frac{9}{8}\times\frac{9}{8}\times\frac{9}{8}10800×
8
9
×
8
9
×
8
9
= 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}2
2
1
years, Rate of interest (R) = 10% p.a.
Amount(A) = P\left(1+\frac{R}{100}\right)^nP(1+
100
R
)
n
= 18000\left(1+\frac{10}{100}\right)^2=18000\left(1+\frac{1}{10}\right)^218000(1+
100
10
)
2
=18000(1+
10
1
)
2
= 18000\left(\frac{11}{10}\right)^2=18000\times\frac{11}{10}\times\frac{11}{10}18000(
10
11
)
2
=18000×
10
11
×
10
11
= Rs. 21,780
Interest for \frac{1}{2}
2
1
years on Rs. 21,780 at rate of 10% = \frac{21780\times10\times1}{100}
100
21780×10×1
= Rs. 1089
Total amount for 2\ \frac{1}{2}2
2
1
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}1
2
1
=
2
3
years = 3 years
Rate of interest (R) = 8% = 4% (compounded half yearly)
Amount (A) = P\left(1+\frac{R}{100}\right)^nP(1+
100
R
)
n
= 62500\left(1+\frac{4}{100}\right)^2(1+
100
4
)
2
= 62500\left(1+\frac{1}{25}\right)^3(1+
25
1
)
3
= 62500\left(\frac{26}{25}\right)^3(
25
26
)
3
= 62500 \times\frac{26}{25}\times\frac{26}{25}\times\frac{26}{25}×
25
26
×
25
26
×
25
26
= Rs. 70,304
Compound Interest (C.I.) = A – P
= Rs. 70304 – Rs. 62500 = Rs. 7,804