Investment required for a target income with brokerage What investment is required to obtain an income of $1938 from 9.5% stock quoted at 90, if brokerage on purchase is 1%?

Introduction / Context:To secure a target dividend, first determine the required nominal amount. Then convert that nominal into an investment using the effective purchase price per $100, including brokerage.

Given Data / Assumptions:

• Target income = $1938
• Coupon rate = 9.5% ⇒ dividend per $100 nominal = $9.50
• Quoted price = 90 per $100 nominal
• Brokerage on purchase = 1% (on market price)

Concept / Approach:Nominal needed N satisfies 0.095 * N = 1938 ⇒ N. Investment = (N/100) * (quote + brokerage% of quote).

Step-by-Step Solution:N = 1938 / 0.095 = $20,400 nominalEffective per-100 price = 90 + (1% of 90) = 90 + 0.9 = $90.9Investment = (20400/100) * 90.9 = 204 * 90.9 = $18,543.60

Verification / Alternative check:Check income: 9.5% of 20,400 = 1,938, matching the target.

Why Other Options Are Wrong:The other amounts correspond to misapplied brokerage or rounding; $18,543.60 is exact from the given data.

Common Pitfalls:Computing nominal from price rather than from dividend; forgetting to include brokerage in effective price.

Final Answer:$ 18543.60