Question

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 %

Answer 1

Answer:

Additional $1,750 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 $1,750 must be invested by Ben.