Mathematics for FinanceMTP Dec 23 Series IIQuestion 3955 of 507
All Questions

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
For any discrepancies in this question, email contact@cadada.in

Correct Answer

Option b5.81\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

Let the principal be P\displaystyle P. Given parameters: * Nominal rate of interest (r\displaystyle r) = 12%\displaystyle 12\% p.a. =0.12\displaystyle = 0.12 * Compounding frequency (m\displaystyle m) = 12\displaystyle 12 (compounded monthly) * Monthly rate (i\displaystyle i) = 0.1212=0.01\displaystyle \frac{0.12}{12} = 0.01 We want to find the number of years (t\displaystyle t) for the principal to double: A=P(1+i)12tA = P(1+i)^{12t} 2P=P(1.01)12t2P = P(1.01)^{12t} (1.01)12t=2(1.01)^{12t} = 2 Taking natural logarithms on both sides: 12tln(1.01)=ln(2)12t \ln(1.01) = \ln(2) 12t0.6931470.00995069.66 months12t \approx \frac{0.693147}{0.009950} \approx 69.66 \text{ months} Solving for t\displaystyle t: t69.66125.81 yearst \approx \frac{69.66}{12} \approx 5.81 \text{ years} Thus, it will take approximately 5.81\displaystyle 5.81 years to double. Hence, **Option B** is the correct answer.

More Questions from Mathematics for Finance

Ready to Master Mathematics for Finance?

Practice all 507 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free