Question

Suppose you have $1300 deposited at 4.75% compounded monthly. About long will it take your

balance to increase to $3200?

Answer 1

20 months

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 =
`log_(2) (8)` = 3 (take note that the 2 goes in subscript, whereas the 8 goes in the brackets)

Now to apply this to our problem:

t =
`log_(1.0475)((32)/(13))` = ~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.