What is the interest rate necessary for an investment to quadruple after 7 7 years of continuous compound​ interest?

Question

please help me solve this question

Answer 1

 

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For non-continuous compounding, future value can be found by this:

 

F = P(1+r/n)^nt

 

Where F = Future value

          P = Present value

          n = compounding periods per year

          r = interest rate (as a decimal)

          t = number of years

 

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For continuous compounding you let n—>∞ in the above equation.   When you do that, you get:

 

       F = Pe^rt

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For a quadrupling of P:

 

       4P = Pe^r(77)

         4 = e^r(77)

        ln(4) = 77r

             r = ln(4)/77 = 0.01800   

 

 Ans:  1.8% 

 

I wasn't 100% sure that was 77 years.  If I was wrong about the time span just substitute the correct number.

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Sanity check:  e^77*0.018 = 3.9988 ≈ 4 

 

 

Answer 2

P exp(7r) = 4P

 

 exp(7r) = 4

 

 7r = ln 4

 

 r = ln 4/7 = 0.1981