| What sum invested for 1½ years, compounded half yearly at the rate of 4% p.a., amounts to Rs. 1,32,651?
Please scroll down to see the correct answer and solution guide.
Right Answer is: D
SOLUTION
Given
Amounts = Rs. 1,32,651
Time = 3/2 years
Rate = 4%
Compounded half yearly
Concept
A = P × (1 + r/100)t
When compounded half yearly
Rate become half and Time become double (As in 1 year 12 months = 6 months + 6 months)
Calculation
Time = 3 years
Rate = 2%
⇒ 132651 = P × (1 + (2/100))3
⇒ 132651 = P × (1 + (1/50))3
⇒ 132651 = P × (51/50)3
⇒ P = (132651 × 50 × 50 × 50)/(51 × 51 × 51)
Note:- 513 = 132651
⇒ P = Rs. 125000
∴ Sum = Rs. 125000
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Solution
The correct option is B
₹13891.5
In compound Interest A = P(1+R100)n
Given,
P = ₹12000
T = 1.5 years = 3 half-years
(∵ the interest is compounded half−yearly,so T =1.5×2)
R = 5% (∵ the interest is compounded half−yearly,so R =102)
A
=12000×[1+102×100]3
A = ₹13891.5
Textbooks
Question Papers
Home
Given
Amount (A) = Rs 140608
Rate (R) = 8% p.a. = 4% half-yearly
Period (n) ==1 \frac{1}{2} \text { years } = 3 half-year
A = P {1 + (R / 100)}n
140608 = P {1 + (4 / 100)}3
140608 = P (26 / 25)3
Therefore,
P = 140608 × (25 / 26) × (25 / 26) × (25 / 26)
On further calculation, we get,
P = Rs 125000
Hence,
Principal = Rs 125000