A professor wants to supplement her pension with investment interest. If she invests $26,000 at 4% interest, how much more would she have to invest at 7% to achieve a goal of $2,300 per year in supplemental income?
To determine how much more the professor would have to invest at 7% interest to achieve a goal of $2,300 per year in supplemental income, we need to calculate the amount of interest generated by the $26,000 at 4% interest.
Step 1: Calculate the interest earned on the initial investment at 4%:
Interest = Principal x Rate
Interest = $26,000 x 0.04
Interest = $1,040
Step 2: Determine the difference between the desired supplemental income and the interest earned at 4%:
Difference = Desired supplemental income - Interest earned at 4%
Difference = $2,300 - $1,040
Difference = $1,260
Step 3: Calculate the additional investment required at 7% interest to generate the difference as interest income:
Additional Investment = Difference / Rate
Additional Investment = $1,260 / 0.07
Additional Investment ≈ $18,000
Therefore, the professor would need to invest approximately $18,000 at 7% interest to achieve her goal of $2,300 per year in supplemental income.