Question
Download Solution PDFIn how many months, at a rate of 6% compound interest per annum, will a sum of ₹1,200 become ₹1,348.32.?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Principal (P) = ₹1,200
Amount (A) = ₹1,348.32
Rate of interest (R) = 6% per annum
Formula Used:
Compound Interest Formula: A = P \((1 + \frac{R}{100})^n\)
Calculation:
We need to find the number of months (n).
Given:
₹1,348.32 = ₹1,200 \((1 + \frac{6}{100} )^\frac{n}{12}\)
⇒ 1.1236 = \((1.06)^\frac{n}{12}\)
Taking natural logarithm on both sides:
\(ln(1.1236) = \frac{n}{12} × ln(1.06)\)
⇒ \(\frac{n}{12} = ln(1.1236) / ln(1.06)\)
⇒ \(\frac{n}{12} = 0.1167 / 0.0583\)
⇒ \(\frac{n}{12} = 2\)
⇒ n = 2 × 12
⇒ n = 24
Hence, the number of months required is 24 months.
Alternate Method Given:
Principal = ₹1200
Amount = ₹1348.32
Rate = 6% per annum
Calculations:
A = P × (1.06)t
Start multiplying year by year until we reach 1348.32
Year 1: 1200 × 1.06 = 1272
Year 2: 1272 × 1.06 = 1348.32
∴ Time = 2 years = 24 months
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