Answer:
Additional <u>$1,750 </u>must be invested by Ben.
Explanation:
Note: The question is not complete as some dots are omitted. The question is therefore given correctly before answering it as follows:
If Ben invests $3500 at 4% interest per year, how much additional money must he invest at 5 1/2 % annual interest to ensure that the interest he receives each year is 4 1/2 %.
The question is now answered as follows:
From the question, we have:
Initial amount invested = $3,500
Interest rate on initial amount invested = 4%, or 0.04
Interest amount from initial amount invested = Initial amount invested * Interest rate on initial amount invested = $3,500 * 4% = $140
Let y represents the additional amount to invest. Therefore, we have:
Interest rate of additional amount invested = 5 1/2% = 5.5% = 0.055
Interest amount from additional amount invested = y * Interest rate of additional amount invested = y * 0.055 = y0.055
Total interest amount = Interest amount from initial amount invested + Interest amount from additional amount invested = $140 + y0.055
New amount invested = Initial amount invested + y = $3,500 + y
Interest rate of new amount invested = 4 1/2% = 4.5% = 0.045
Interest amount from new amount invested = New amount invested * ($3,500 + y) * 0.045 = $157.50 + y0.045
Since total interest amount must equal interest amount from new amount invested, we equate the two and solve as follows:
Total interest amount = Interest amount from new amount invested
$140 + y0.055 = $157.50 + y0.045
We can now solve for y as follows:
y0.055 - y0.045 = $157.50 - $140
y0.01 = $17.50
y = 17.50 / 0.01
y = $1,750
Therefore, additional <u>$1,750 </u>must be invested by Ben.
