Question

Mrs. Williams put $500 into a retirement account that earns 4% interest. How long will it take for there to be $3,500?

Answer 1

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Answer:

  A = 500

  B = 1.04

  49.6 years

Step-by-step explanation:

We assume your 'A' and 'B' refer to parameters in an exponential formula of the form ...

  y = A·B^x

In this form, A is the initial investment value, $500. B is the growth factor, 1+4% = 1.04, assuming interest is compounded annually. We want to find x such that y=$3500.

  3500 = 500·1.04^x . . . . . fill in known values

  7 = 1.04^x . . . . . . . . . . . . . divide by 500

  log(7) = x·log(1.04) . . . . . . take logarithms

  x = log(7)/log(1.04) ≈ 49.61 . . . . divide by the coefficient of x

It will take about 49.6 years for there to be $3500 in Mrs. Williams's account.