Question

The difference between the simple and the compound interest compunded every six months at the rate of 10 percent per annum at the end of two years is rs 124.05. what is the sum?

Answer 1

und interest, amount after two years
=
P
(
1
+
R
/
2
100
)
(
2
T
)
=
P
(
1
+
10
/
2
100
)
(
2
×
2
)
=
P
(
1
+
5
100
)
4
=
P
(
1
+
1
20
)
4
=
P
(
21
20
)
4
=P(1+R/2100)(2T)=P(1+10/2100)(2×2)=P(1+5100)4=P(1+120)4=P(2120)4

Compound interest =
P
(
21
20
)
4
−
P
=
P
[
(
21
20
)
4
−
1
]
P(2120)4−P=P[(2120)4−1] ----(1)

Simple Interest =
PRT
100
=
P
×
10
×
2
100
=
P
5
PRT100=P×10×2100=P5 ----(2)

Difference between compound interest and simple interest is given as Rs.496.20

P
[
(
21
20
)
4
−
1
]
−
P
5
=
496.20
P
[
(
21
20
)
4
−
1
−
1
5
]
=
496.20
P
[
194481
160000
−
1
−
1
5
]
=
496.20
P
[
194481
−
160000
−
32000
160000
]
=
496.20
2481
P
160000
=
496.20
P[(2120)4−1]−P5=496.20P[(2120)4−1−15]=496.20P[194481160000−1−15]=496.20P[194481−160000−32000160000]=496.202481P160000=496.20

P =
496.20×160000/2481
p= 32000

Answer 2

Let Principal = P, Rate = R% per annum, Time = n years.
Compound Interest, CI=P(1+R/100)n - P , if compound interest is payable annually
Simple Interest (SI) = (P*R*T )/100
Then, [ P(1 +5/100)4 - P] - [(P x 10 x 2)/100 ] = 124.05
Solving the above equation,we get P = Rs. 800