5 Principal Rs.6,000 for 12 years at 10% per annum. Find the following:
ii) compound interest is
A) Rs. 903
B) Rs. 909
C) Rs. 900
D) Rs. 930
Answers
Answer:375
Step-by-step explanation:
Let the sum be Rs.x
Amount after 3 years on Rs.x at 20% per annum when interest is compounded annually
=
P
(
1
+
R
100
)
T
=
x
(
1
+
20
100
)
3
=
x
(
120
100
)
3
=
x
(
6
5
)
3
Compound Interest =
x
(
6
5
)
3
−
x
=
x
[
(
6
5
)
3
−
1
]
=
x
[
216
125
−
1
]
=
91
x
125
Simple Interest =
PRT
100
=
x
×
20
×
3
100
=
3
x
5
=P(1+R100)T=x(1+20100)3=x(120100)3=x(65)3Compound Interest = x(65)3−x=x[(65)3−1]=x[216125−1]=91x125Simple Interest = PRT100=x×20×3100=3x5
Given that difference between compound interest and simple interest is Rs.48
91
x
125
−
3
x
5
=
48
91
x
−
75
x
125
=
48
16
x
125
=
48
x
=
48
×
125
16
=
3
×
125
=
Rs. 375
91x125−3x5=4891x−75x125=4816x125=48x=48×12516=3×125=Rs. 375
i.e, the sum is Rs.375
--------------------------------------------------------------------------------------
Solution 2
---------------------------------------------------------------------------------------
The difference between compound interest and simple interest on Rs. P for 3 years at R% per annum
=
P
(
R
100
)
2
(
R
100
+
3
)
=P(R100)2(R100+3)
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P
(
R
100
)
2
(
R
100
+
3
)
=
48
P
(
20
100
)
2
(
20
100
+
3
)
=
48
P
(
1
5
)
2
(
1
5
+
3
)
=
48
P
(
1
25
)
(
16
5
)
=
48
P
=
48
×
25
×
5
16
=
3
×
25
×
5
=
375