Answer:
20 months
Step-by-step explanation:
Let's write an equation to describe the compound increase:
C = 1300 * 1.0475^t (where C = money in account, t = number of months)
Now, we need C to equal 3200, so let's do that:
3200 = 1300 * 1.0475^t
Divide both sides by 1300:
32/13 = 1.0475^t
This part is tricky, but to isolate t we can use logarithms. Here's an example:
2^x = 8 (2 to the power of what is 3?)
x = [tex]log_{2} (8)[/tex] = 3 (take note that the 2 goes in subscript, whereas the 8 goes in the brackets)
Now to apply this to our problem:
t = [tex]log_{1.0475}(\frac{32}{13})[/tex] = ~19.411
We need to round up here, as we cannot pass only a fraction of a month and 19 months is not enough (you will have $3,139.57), so the answer is 20 months.
