Question
Download Solution PDFA sum of ₹x amounts to ₹54571 in \(2 \frac{1}{2}\) years at 12% p.a., interest compounded after every 10 months. What is the value of x?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula Used:
A = P × (1 + R/100)n
Calculation:
Let P = x
Since interest is compounded every 10 months, number of compounding periods in 2.5 years = (30 months / 10 months) = 3
Effective rate for 10 months = 12 × (10 / 12) = 10%
So,
A = x × (1 + 10/100)3
54571 = x × (110/100)3
54571 = x × (1331 / 1000)
x = 54571 × (1000 / 1331)
x = 41000
The correct value of x is ₹41000
Shortcut Trick
10% = 1/10
p : A = 10 : 11
Repeated 3 times:
10 : 11
10 : 11
10 : 11
_________
1000 : 1331
According to the question:
1331 unit = 54571
1 unit = 54571 / 1331 = 41
Then principal = 1000 unit = 41000
Last updated on Jun 30, 2025
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