An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Calculate the weighted ROR for Portfolio 1: approximately 2.25%.
Calculate the weighted ROR for Portfolio 2: approximately 3.53%.
Calculate the weighted ROR for Portfolio 3: approximately 2.28%.
Rank the portfolios from best to worst: Portfolio 2, Portfolio 3, Portfolio 1. The answer is Portfolio 2, Portfolio 3, Portfolio 1. P or t f o l i o 2 , P or t f o l i o 3 , P or t f o l i o 1
Explanation
Understanding the Problem We are given a table with the Rate of Return (ROR) and corresponding investment amounts for three portfolios. Our goal is to calculate the weighted average ROR for each portfolio and then rank them from best to worst performance.
Weighted ROR Formula To calculate the weighted average ROR for each portfolio, we use the formula:
Weighted ROR = ∑ I n v es t m e n t i ∑ ( RO R i × I n v es t m e n t i )
Portfolio 1 Calculation First, let's calculate the weighted ROR for Portfolio 1. The RORs are -3.8%, 2.1%, 11.3%, 5.8%, and 1.6%, and the corresponding investments are $700, $2,575, $220, $1,000, and $1,430. The total investment is $700 + $2,575 + $220 + $1,000 + $1,430 = $5,925.
The weighted ROR is:
5925 ( − 0.038 × 700 ) + ( 0.021 × 2575 ) + ( 0.113 × 220 ) + ( 0.058 × 1000 ) + ( 0.016 × 1430 ) = 5925 − 26.6 + 54.075 + 24.86 + 58 + 22.88 = 5925 133.295 ≈ 0.0225 or 2.25%
Portfolio 2 Calculation Next, let's calculate the weighted ROR for Portfolio 2. The RORs are -3.8%, 2.1%, 11.3%, 5.8%, and 1.6%, and the corresponding investments are $1,250, $1,700, $1,515, $1,345, and $1,675. The total investment is $1,250 + $1,700 + $1,515 + $1,345 + $1,675 = $7,485.
The weighted ROR is:
7485 ( − 0.038 × 1250 ) + ( 0.021 × 1700 ) + ( 0.113 × 1515 ) + ( 0.058 × 1345 ) + ( 0.016 × 1675 ) = 7485 − 47.5 + 35.7 + 171.295 + 78.01 + 26.8 = 7485 264.355 ≈ 0.0353 or 3.53%
Portfolio 3 Calculation Now, let's calculate the weighted ROR for Portfolio 3. The RORs are -3.8%, 2.1%, 11.3%, 5.8%, and 1.6%, and the corresponding investments are $1,025, $500, $790, $250, and $2,500. The total investment is $1,025 + $500 + $790 + $250 + $2,500 = $5,065.
The weighted ROR is:
5065 ( − 0.038 × 1025 ) + ( 0.021 × 500 ) + ( 0.113 × 790 ) + ( 0.058 × 250 ) + ( 0.016 × 2500 ) = 5065 − 38.95 + 10.5 + 89.27 + 14.5 + 40 = 5065 115.37 ≈ 0.0228 or 2.28%
Ranking the Portfolios Comparing the weighted RORs, we have:
Portfolio 1: 2.25% Portfolio 2: 3.53% Portfolio 3: 2.28%
Ranking the portfolios from best to worst performance, we get: Portfolio 2, Portfolio 3, Portfolio 1.
Final Answer Based on the calculations, the correct order of portfolio performance from best to worst is Portfolio 2, Portfolio 3, Portfolio 1.
Examples
Understanding weighted averages is crucial in finance. For example, when evaluating investment portfolios, different assets contribute differently to the overall return. A weighted average helps to accurately measure the portfolio's performance by considering the proportion of each asset. This concept extends to everyday life, such as calculating your grade in a class where assignments have different weights or determining the average price of a basket of goods with varying quantities.
By using the formula Q = I × t with a current of 15.0 A over 30 s , the total charge calculated is 450 C . Dividing this by the charge of an electron, approximately 2.81 × 1 0 21 electrons flow through the device.
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