A sum of $4000 is invested at 5.5% interest per year. Find the amount of time needed to double the money if it’s compounded monthly. A) 12y
B) 12y 4m
C) 12y 8m
D) 13y

9514 1404 393

  C)  12y 8m

Step-by-step explanation:

The amount of principal P at compound monthly at interest rate r per year is given by ...

  A = P(1 +r/12)^(12t) . . . . after t years

Here, we want to find t, so ...

  A/P = (1 +r/12)^(12t)

  log(A/P) = (12t)·log(1 +r/12)

  t = log(A/P)/(12·log(1 +r/12))

Filling in the given values, we find t to be ...

  t = log(8000/4000)/(12·log(1 +0.055/12)) ≈ 12.6315 ≈ 12 years 7.6 months

It will take about 12 years 8 months to double the money.

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: )

step-by-step explanation: