An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
A device delivering 15.0 A for 30 seconds transfers approximately 2.81 × 1 0 21 electrons. This is calculated by first determining the total charge using Q = I × t , resulting in 450.0 C, and then dividing by the charge of a single electron. Ultimately, this process demonstrates how to convert current and time into a quantity of electrons.
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Calculate the total amount paid for each loan by multiplying the monthly payment by the loan term.
Calculate the finance charge for each loan by subtracting the principal from the total amount paid.
Compare the finance charges for each loan option.
Order the loans from least to greatest finance charge: Z < X < Y .
Explanation
Understanding the Problem We are given three loan options with different principal amounts, monthly payment amounts, and loan terms. Our goal is to determine the order of these loan options from the least finance charge to the greatest finance charge. The finance charge is the total interest paid over the life of the loan.
Calculating Finance Charges To find the finance charge for each loan, we first calculate the total amount paid over the loan term by multiplying the monthly payment by the number of months in the term. Then, we subtract the principal amount from the total amount paid.
Finance Charge for Option X For Loan Option X: Principal: $14,000.00 Monthly Payment: 324.32 L o an T er m : 48 m o n t h s T o t a lP ai d = M o n t h l y P a y m e n t \times$ Loan Term = $324.32 \times 48 = $15,567.36 Finance Charge = Total Paid - Principal = $15,567.36 - $14,000.00 = $1,567.36
Finance Charge for Option Y For Loan Option Y: Principal: $14,000.00 Monthly Payment: 264.12 L o an T er m : 60 m o n t h s T o t a lP ai d = M o n t h l y P a y m e n t \times$ Loan Term = $264.12 \times 60 = $15,847.20 Finance Charge = Total Paid - Principal = $15,847.20 - $14,000.00 = $1,847.20
Finance Charge for Option Z For Loan Option Z: Principal: $15,000.00 Monthly Payment: 332.69 L o an T er m : 48 m o n t h s T o t a lP ai d = M o n t h l y P a y m e n t \times$ Loan Term = $332.69 \times 48 = $15,969.12 Finance Charge = Total Paid - Principal = $15,969.12 - $15,000.00 = $969.12
Ordering the Options Comparing the finance charges: Option X: $1,567.36 Option Y: $1,847.20 Option Z: $969.12 Ordering from least to greatest finance charge, we have Option Z < Option X < Option Y.
Examples
When taking out a loan, it's important to understand the finance charges, which represent the total cost of borrowing money beyond the principal amount. This problem illustrates how to calculate and compare finance charges for different loan options. In real life, understanding these calculations can help you make informed decisions about which loan is the most cost-effective for your needs, whether it's for a car, a house, or a personal expense. By comparing the total cost, you can choose the loan that saves you the most money over the long term.
