Mathematics for FinanceMTP Dec 23 Series IIQuestion 1404 of 512
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How long will it take for a principal to double if money is worth 12%\displaystyle 12\% compounded monthly?

Options

A4.25\displaystyle 4.25 years
B5.81\displaystyle 5.81 years
C6.93\displaystyle 6.93 years
DNone of these
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Correct Answer

✅ Option b — 5.81\displaystyle 5.81 years

All Options:

  • A4.25\displaystyle 4.25 years
  • B5.81\displaystyle 5.81 years
  • C6.93\displaystyle 6.93 years
  • DNone of these

Detailed Solution & Explanation

**Derivation of Time to Double Sum** Given: - Nominal rate (r\displaystyle r) = 12%\displaystyle 12\% per annum compounded monthly - Let the principal be P\displaystyle P. We want the amount to double (A=2P\displaystyle A = 2P). **Step 1: Calculate monthly interest rate (i\displaystyle i)** i=r12=12%12=1%=0.01 per monthi = \frac{r}{12} = \frac{12\%}{12} = 1\% = 0.01 \text{ per month} **Step 2: Set up the compounding equation** A=P(1+i)nA = P(1 + i)^n 2P=P(1+0.01)n2P = P(1 + 0.01)^n 2=(1.01)n2 = (1.01)^n **Step 3: Solve for n\displaystyle n (months) using logarithms** ln⁡(2)=nln⁡(1.01)\ln(2) = n \ln(1.01) n=ln⁡(2)ln⁡(1.01)n = \frac{\ln(2)}{\ln(1.01)} Using log values: ln⁡(2)≈0.693147\ln(2) \approx 0.693147 ln⁡(1.01)≈0.0099503\ln(1.01) \approx 0.0099503 n=0.6931470.0099503≈69.66 monthsn = \frac{0.693147}{0.0099503} \approx 69.66 \text{ months} **Step 4: Convert months to years** Years=69.6612≈5.815 years\text{Years} = \frac{69.66}{12} \approx 5.815 \text{ years} Hence, **Option B** is the correct answer.

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A certain sum of money was put at S.I. for 2.5\displaystyle 2.5 years at a certain rate of S.I. p.a. Had it been put at 4%\displaystyle 4\% higher rate, it would have fetched 500\displaystyle 500 more. Find the sum of money.

Rs.1,25,000\displaystyle 1,25,000 is borrowed at compound interest at the rate of 2%\displaystyle 2\% for the 1st year, 3%\displaystyle 3\% for the second year and 4%\displaystyle 4\% for the 3rd year. Find the amount to be paid after 3 years.

If Rs. 1,000\displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every 10\displaystyle 10 years, then the number in years in which it will amount to Rs. 2,000\displaystyle \text{Rs. }2,000 is:

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