Mathematics for FinancePYQ Jun 24Question 1476 of 512
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At 8%\displaystyle 8\% compounded annually, how long will it take 750\displaystyle 750 to double?

Options

A6.5\displaystyle 6.5 years
B48\displaystyle 48 months
C9\displaystyle 9 years
D12\displaystyle 12 years
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Correct Answer

✅ Option c — 9\displaystyle 9 years

All Options:

  • A6.5\displaystyle 6.5 years
  • B48\displaystyle 48 months
  • C9\displaystyle 9 years
  • D12\displaystyle 12 years

Detailed Solution & Explanation

To find how long it takes for a principal sum P\displaystyle P to double under compound interest, we use the compound interest formula: A=P(1+i)nA = P(1 + i)^n Given: * Future Amount (A\displaystyle A) = 2P\displaystyle 2P * Interest rate (i\displaystyle i) = 8%\displaystyle 8\% p.a. = 0.08\displaystyle 0.08 Substituting these values into the formula: 2P=P(1+0.08)n2P = P(1 + 0.08)^n 2=(1.08)n2 = (1.08)^n Taking natural logarithms on both sides: ln⁡(2)=nln⁡(1.08)\ln(2) = n \ln(1.08) 0.693147=n×0.0769610.693147 = n \times 0.076961 n=0.6931470.076961≈9.006 yearsn = \frac{0.693147}{0.076961} \approx 9.006 \text{ years} Thus, it takes approximately 9\displaystyle 9 years for the investment to double. Hence, **Option C** is the correct answer.

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