1. Henry's brokerage fees if his income doubles are $360.
2. The amount of income Henry uses for everything else is $2,000.
3. Henry pays $4,320 in brokerage fees per year.
4. Henry invests $31,680 in the mutual fund per year after fees.
5. Henry's brokerage fees if his income triples are $540.
Let's break down each part of the question:
1. Henry's brokerage fees if his income doubles:
Henry's monthly income is $5,000. If his income doubles, it becomes $5,000 * 2 = $10,000.
The amount to be invested in the mutual fund is 30% of his monthly income, so for the doubled income:
0.30×$10,000=$3,000
The brokerage fee is 12% of the amount invested:
0.12×$3,000=$360
Therefore, Henry's brokerage fees if his income doubles are $360.
2. The amount of income Henry uses for everything else:
If Henry invests 30% of his monthly income, the remaining amount for everything else is:
$5,000−$3,000=$2,000
Therefore, the amount of income Henry uses for everything else is $2,000.
3. The amount of brokerage fees Henry pays per year:
The monthly brokerage fees are $360, and there are 12 months in a year:
$360×12=$4,320
Therefore, Henry pays $4,320 in brokerage fees per year.
4. The amount of money Henry invests after fees per year:
Henry invests $3,000 per month, and the annual investment is
$3,000×12=$36,000.
After deducting the annual brokerage fees ($4,320):
$36,000−$4,320=$31,680
Therefore, Henry invests $31,680 in the mutual fund per year after fees.
5. Henry's brokerage fees if his income triples:
If Henry's income triples, it becomes
$5,000×3=$15,000.
The amount to be invested in the mutual fund is 30% of his monthly income:
0.30×$15,000=$4,500
The brokerage fee is 12% of the amount invested:
0.12×$4,500=$540
Therefore, Henry's brokerage fees if his income triples are $540.