A prfessor wants to supplement her pension with investment interst. If she invest $28,000 at 6%, how much more would she have to invest at 7% to achieve a goal of %3,500 per year in supplemental income?
28000(1.06) + x(1.07) = 3500
solve for x
just looked at my answer again, and it looks like I messed up
should have said:
28000(.06) + x(.07) = 3500
the answer is 26000
To find out how much more the professor would have to invest at 7% to achieve a goal of $3,500 per year in supplemental income, we can follow these steps:
Step 1: Calculate the income from the initial investment at 6%
The income from the $28,000 investment at 6% can be calculated using the formula:
Income = Principal * Rate
Income = $28,000 * 0.06
Income = $1,680
Step 2: Calculate the additional income needed
To achieve the goal of $3,500 per year in supplemental income, the professor would need an additional income of:
Additional income = Goal income - Income from previous investment
Additional income = $3,500 - $1,680
Additional income = $1,820
Step 3: Calculate the amount needed to be invested at 7%
To calculate the amount needed to be invested at 7% to generate the additional income of $1,820, we can use the formula:
Principal = Income / Rate
Principal = $1,820 / 0.07
Principal ≈ $26,000
Therefore, the professor would need to invest approximately $26,000 at 7% to achieve a goal of $3,500 per year in supplemental income.