How do I find the aggressive growth?

Question

Divide the given investors money into the five categories as to position them right at the middle of the recommended ranges. Candace Cooney; in her high income/saving years, invested an amount of $200,000 . Aggressive growth of 2-5%, growth of 23-31%, growth & income of 28-40%, income of 24-35%, and cash at 4-9%.

Answer 1

To position Candace in the middle of each recommended range, first find the midpoint percentage for each category.

Aggressive growth:

(2% + 5%)/2 = 3.5%

Growth:

(23% + 31%)/2 = 27%

Growth & income:

(28% + 40%)/2 = 34%

Income:

(24% + 35%)/2 = 29.5%

Cash:

(4% + 9%)/2 = 6.5%

Notice these percentages total:

3.5% + 27% + 34% + 29.5% + 6.5% = 100.5%

Since they total 100.5% rather than 100%, the midpoint recommendations cannot all be used exactly while investing precisely $200,000. A common way to handle this is to normalize the percentages so they total 100%.

For aggressive growth:

(3.5 / 100.5) × $200,000 = $6,965.17

Doing the same for each category gives approximately:

Aggressive growth: $6,965.17

Growth: $53,731.34

Growth & income: $67,661.69

Income: $58,706.47

Cash: $12,935.32

These total approximately $200,000.

If the exercise simply expects you to multiply $200,000 by each unadjusted midpoint, then aggressive growth would be:

$200,000 × 3.5% = $7,000

But those five unadjusted amounts total $201,000, so the problem's stated ranges contain a small inconsistency.