Question

Ashley deposits $500 into an account that earns 2% interest compounded 3 times per year. How much money will Ashley have in her account after 4 years?

Answer 1

Note that the 2% is not stated as "per annum" (per year)

Based on 2% per year `->$541.50` rounded to 2 decimal places
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`color(magenta)(" This one is not very likely!")`
Based on 2% per `1/3` year `->$634.12` rounded to 2 decimal places.

Explanation:

`color(red)("Assumption: the 2% is per annum")`

`=>P(1+2/(100xx3))^(3n)` where `n` is the number of years

and the `2/(100xx3)` converts the percentage to `1/3` year equivalent.

`=>$500(302/300)^(3xx4)`

`=$541.4997 ~~$541.50` rounded to 2 decimal places

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`color(red)("Assumption: the 2% is per "1/3 " year")`

`=>P(1+2/100)^(3n)` where `n` is the number of years

`=>$500(102/100)^(3xx4)`

`=$634.1208~~$634.12` rounded to 2 decimal places.