Your business requests a 3-month loan for 550,000. What will be the interest paid at the end of the term if the business risk percentage is assessed at $2.0\%$ and LIBOR is at $2.1\%$? $\text { Interest Paid } =\$[?] Round to the nearest hundredth.
Answer (2)
Calculate the total interest rate: 2.0% + 2.1% = 4.1% .
Calculate the annual interest: $550 , 000 × 0.041 = $22 , 550 .
Calculate the 3-month interest: $22 , 550 × 12 3 = $5 , 637.50 .
The interest paid at the end of the term is $5 , 637.50 .
Explanation
Understanding the Problem We are given a problem where a business is taking out a 3-month loan of $550,000. The interest rate is determined by adding the business risk percentage (2.0%) and the LIBOR rate (2.1%). Our goal is to calculate the total interest paid at the end of the 3-month term, rounded to the nearest hundredth.
Calculating Total Interest Rate First, we need to calculate the total interest rate by adding the business risk percentage and the LIBOR rate: Total Interest Rate = Business Risk Percentage + LIBOR Rate
Total Interest Rate = 2.0% + 2.1% = 4.1%
Calculating Annual Interest Next, we calculate the annual interest by multiplying the loan amount by the total interest rate: Annual Interest = Loan Amount × 100 Total Interest Rate
Annual Interest = $550 , 000 × 100 4.1 = $550 , 000 × 0.041 = $22 , 550
Calculating 3-Month Interest Now, we calculate the interest for the 3-month term. Since the loan is for 3 months, which is 12 3 or 4 1 of a year, we multiply the annual interest by this fraction: 3-Month Interest = Annual Interest × 12 3
3-Month Interest = $22 , 550 × 12 3 = $22 , 550 × 0.25 = $5 , 637.50
Final Answer Finally, we round the 3-month interest to the nearest hundredth, which is already done in this case: Interest Paid = $5 , 637.50
Examples
Understanding loan interest calculations is crucial in personal and business finance. For example, when taking out a mortgage for a house, knowing how the interest rate affects the total amount paid over the loan's lifetime helps in making informed financial decisions. Similarly, businesses use these calculations to evaluate the cost of borrowing money for investments or operations, ensuring they can manage their finances effectively and make profitable decisions.
The interest paid at the end of the 3-month loan of $550,000 is calculated by first determining the total interest rate of 4.1%. The annual interest amounts to $22,550, and for 3 months, this results in an interest payment of $5,637.50.
;
