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Compute the doubling time (in years) associated to an annual compound interest rate of 6.5%.

User Aky
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1 Answer

6 votes

Answer:

11 years

Explanation:

Formula for annual compound interest:
A=P(1+r)^t. In context of this problem, P and A are not relevant as they aren't mentioned. So, the equation we want to end up solving is
2=(1+r)^t, where t is the unknown variable we're solving for, and r = .065. We desire to double the amount, A, so the left side of the equation is set to 2.

  1. Set up the equation:

    2=(1+.065)^t\\ > 2=1.065^t
  • To solve this, you should know the format of a basic logarithm:

    b^x=a < - > log_(b)a=x.

2. Set up the logarithm and solve:



  • 1.065^t=2\\log_(1.065)(2)=t\\t= 11.00673904

t = 11 years

As a side note that may be irrelevant if this is a math course, economists often use the "rule of 72" for compound interest doubling time. Meaning
(72)/(r) returns the doubling time in years. 72/6.5 gives us ≈ 11.079, or 11 years as well.

User Jeroen Wienk
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