Income from a premium purchase – nominal inferred from investment Find the annual income by investing $81,000 in 9% stock quoted at 135.

Introduction / Context:
The income depends on the nominal amount acquired. When buying above par, the same cash buys less nominal. First infer nominal from investment and price, then apply the dividend rate to nominal.

Given Data / Assumptions:

• Investment = $81,000
• Quote = 135 (i.e., $135 per $100 nominal)
• Dividend rate = 9% on nominal

Concept / Approach:
Nominal purchased N satisfies Investment = (N/100) * 135 ⇒ N = Investment * 100 / 135. Income = 9% of N.

Step-by-Step Solution:
N = 81000 * 100 / 135 = $60,000 nominalIncome = 9% of 60,000 = 0.09 * 60,000 = $5,400

Verification / Alternative check:
Per-$100 block: each $135 buys $100 nominal earning $9. With $81,000, that is 600 blocks ⇒ 600 * $9 = $5,400.

Why Other Options Are Wrong:
$6,000 assumes $100,000 nominal; $5,500/$6,400 are not consistent with the 135 quote.

Common Pitfalls:
Applying 9% directly to $81,000; dividends are on nominal, not on cash invested.

Final Answer:
$ 5400