A woman invested in a private company fund, a total sum of Rs. 10,25,000 in the names of her son and daughter aged 13 years and 15 years, respectively, such that they get an equal amount when they are of 18 years. If the company gives 20% compound interest compounded annually, then how much money (in Rs., to the nearest whole number) should be deposited in the name of her son?
- A5,50,500
- B3,55,048
- C4,20,082
- D6,25,000
Solution & Step-by-step Explanation
Let the sum invested in the name of the son be Rs. P
1
and in the name of the daughter be Rs. P
2
.
Time for son to reach 18 years = 18−13=5 years.
Time for daughter to reach 18 years = 18−15=3 years.
According to the question, their amounts at age 18 are equal:
P
1
(1+
100
20
)
5
=P
2
(1+
100
20
)
3
P
1
(
5
6
)
5
=P
2
(
5
6
)
3
P
2
P
1
=
(
5
6
)
5
(
5
6
)
3
=
(
5
6
)
2
1
=
36
25
The total investment is P
1
+P
2
=10,25,000.
The share of the son (P
1
):
P
1
=
25+36
25
×10,25,000
P
1
=
61
25
×10,25,000
P
1
=
61
25,625,000
≈420,081.96
Rounding to the nearest whole number gives Rs. 4,20,082.
1
and in the name of the daughter be Rs. P
2
.
Time for son to reach 18 years = 18−13=5 years.
Time for daughter to reach 18 years = 18−15=3 years.
According to the question, their amounts at age 18 are equal:
P
1
(1+
100
20
)
5
=P
2
(1+
100
20
)
3
P
1
(
5
6
)
5
=P
2
(
5
6
)
3
P
2
P
1
=
(
5
6
)
5
(
5
6
)
3
=
(
5
6
)
2
1
=
36
25
The total investment is P
1
+P
2
=10,25,000.
The share of the son (P
1
):
P
1
=
25+36
25
×10,25,000
P
1
=
61
25
×10,25,000
P
1
=
61
25,625,000
≈420,081.96
Rounding to the nearest whole number gives Rs. 4,20,082.