An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Daniel's ROI remains constant at $500 each year, indicating simple interest.
Claire's ROI increases each year ( $500 , $525 , $551.25 ), suggesting compound interest.
Simple interest is calculated as Principal × Rate × Time , confirming Daniel's 5% simple interest.
Compound interest means earning interest on the principal plus accumulated interest, confirming Claire's 5% compound interest.
Daniel's bank paid simple interest, and Claire's bank paid compound interest. Daniel: Simple Interest, Claire: Compound Interest
Explanation
Understanding the Problem We are given that Daniel and Claire each deposited $10,000 in savings accounts with a 5% annual interest rate. Daniel's return on investment (ROI) remained the same each year, while Claire's increased each year. We need to determine the type of interest each of their banks paid.
Analyzing Daniel's Interest Daniel's ROI is constant at $500 each year. This indicates that he is earning simple interest, where the interest earned is based only on the principal amount.
Analyzing Claire's Interest Claire's ROI increases each year. In Year 1, she earns $500. In Year 2, she earns $525. In Year 3, she earns $551.25. This suggests that she is earning compound interest, where the interest earned is added to the principal, and subsequent interest is calculated on the new principal. Let's verify this by calculating the interest rate for each year.
Confirming Daniel's Simple Interest The interest earned by Daniel is the same each year, which is $500. The initial deposit was 10 , 000. T h es im pl e in t eres t r a t e i sc a l c u l a t e d a s : Simple Interest = Principal × Rate × Time 500 = 10000 × Rate × 1 Rate = 10000 500 = 0.05 = 5% $
This confirms that Daniel earns simple interest at a rate of 5% per year.
Confirming Claire's Compound Interest For Claire, let's calculate the interest earned in Year 2: Interest = Principal × Rate Year 1: 500 = 10000 × 0.05 Year 2: 525 = ( 10000 + 500 ) × 0.05 = 10500 × 0.05 Year 3: 551.25 = ( 10000 + 500 + 525 ) × 0.05 = 11025 × 0.05 This confirms that Claire earns compound interest at a rate of 5% per year.
Final Answer Therefore, Daniel's bank paid simple interest, and Claire's bank paid compound interest.
Examples
Understanding the difference between simple and compound interest is crucial in personal finance. Simple interest is like earning a fixed amount each year on your initial investment, whereas compound interest allows your earnings to grow exponentially as you earn interest on your interest. For example, if you invest $1,000 at a 5% simple interest rate, you'll earn $50 each year. However, if you invest the same amount at a 5% compound interest rate, you'll earn $50 in the first year, $52.50 in the second year (5% of $1,050), and so on, leading to greater returns over time. This concept is widely used in loans, mortgages, and investments, making it essential for making informed financial decisions.
To find the number of electrons flowing through a device with a current of 15.0 A for 30 seconds, we first calculate the total charge using Q = I × t , which gives us 450.0 C. Then, by dividing this charge by the charge of one electron (approximately 1.6 × 1 0 − 19 C ), we find that around 2.81 × 1 0 21 electrons pass through the device. Thus, about 2.81 quintillion electrons flow through the device in that time period.
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