The difference in simple interest and compound interest on a certain sum of money at
% per annum for 3 years is Rs 46. Determine the sum.
Answers
Step-by-step explanation:
Let the sum be Rs.100
Computation of compound interest:
Prinicpal =Rs.100
R=10% per annum and n=2 years.
Amount=Rs.
⎣
⎢
⎡
100×(1+
100
10
)
2
⎦
⎥
⎤
=Rs.
⎣
⎢
⎡
100×(
2
11
) =Rs.121
Computation of simple interest:
Prinicpal =Rs.100
R=10% and Time =2 years.
∴S.I.=Rs.(
100
100×10×2
)=Rs.20
Thus, difference in C.I. and S.I.=Rs.(21−20)=Re.1
Now, if difference between C.I and S.I. is Re.1, Then Sum =Rs.100
If difference between C.I. and S.I. is Rs.500, Then Sum =Rs.(100×500)=Rs.50000
Answer:
Given,
R=6
3
2
%=
3
20
% per annum
T(n)=3 years
C.I. − S.I. =Rs.46
S.I=
100
PTR
=
3×100
P×3×20
=
10
2P
C.I=P[(1+
100
R
)
n
−1]
C.I=P[(1+
3×100
20
)
3
−1]
C.I=P[(
15
16
)
3
−1]
C.I.=P(
3375
4096
−1)
C.I.=P(
3375
4096−3375
)
C.I.=
3375
721P
According to question,
C.I. − S.I. =46
⇒ P(
3375
721
−
10
2
)=46
⇒ P(
6750
1442−1350
)=46
⇒
6750
92P
=46
⇒ P=
92
46×6750