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 total annual interest rate: r = 2.2% + 2.8% = 5% = 0.05 .
Convert the annual interest rate to a monthly interest rate: r m = 12 0.05 .
Calculate the interest paid for the 3-month period: I = 500000 × 12 0.05 × 3 = 6250 .
The interest paid at the end of the 3-month term is 6250.00 .
Explanation
Understanding the Problem We are given a 3-month loan of $500,000 with a business risk percentage of 2.2% and a LIBOR rate of 2.8%. We need to calculate the total interest paid at the end of the term, rounded to the nearest hundredth.
Calculating Total Annual Interest Rate First, we need to find the total annual interest rate by adding the business risk percentage and the LIBOR rate: r = 2.2% + 2.8% = 5% = 0.05
Calculating Monthly Interest Rate Next, we convert the annual interest rate to a monthly interest rate by dividing by 12: r m = 12 0.05 = 0.004166666...
Calculating Total Interest Paid Now, we calculate the interest paid for the 3-month period by multiplying the loan amount by the monthly interest rate and then by 3: I = 500000 × 12 0.05 × 3 = 500000 × 0.004166666... × 3 = 6250
Final Answer Therefore, the interest paid at the end of the 3-month term is $6250.
Examples
Understanding loan interest calculations is crucial in personal and business finance. For instance, if you're planning to take out a mortgage or a business loan, knowing how interest is calculated helps you determine the actual cost of borrowing. This knowledge enables you to compare different loan offers, negotiate better terms, and make informed financial decisions. For example, if you borrow $100,000 at an annual interest rate of 6% for 30 years, calculating the monthly payment and total interest paid over the loan's life helps you understand the long-term financial implications.
The device delivering a current of 15.0 A for 30 seconds transmits about 2.81 billion billion electrons. This is calculated using the relationship between current, charge, and time. Each electron carries a charge of approximately 1.6 × 1 0 − 19 coulombs.
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