At the beginning of the year, you invest $10,000 in an S&P 500 index fund. This fund charges an annual fee of 0.1% of your end-of-year assets at the end of the year. Your friend invests $10,000 in an actively managed fund that charges 1.4% of end-of-year assets at the end of the year. Before fees are taken into account, the index fund is up 9.0% at the end of the year while the actively managed fund is up 9.5%. After fees, how does your performance compare to your friend's?

we can say that we are are $92.40 richer

Explanation:

given data

invest = $10,000

annual fee = 0.1%

index fund = 9.0%

friend invests = $10,000

charges = 1.4%

actively managed fund = 9.5%

to find out

how does your performance compare to your friend's

solution

we get here both performance and than compare by subtract them by each other

first we get here our performance that is = $10,000 * (1 + 9%) * (1-0.1%) ... 1

and friend performance that is $10,000 * (1 + 9.5%) * (1 - 1.4%) ... 2

now subtract equation 1 by 2

= $10,000 * (1 + 9%) * (1-0.1%) - $10,000 * (1 + 9.5%) * (1 - 1.4%)

= $92.40

so we can say that we are are $92.40 richer