Your business requests a 3-month loan for $450,000. 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%?
Interest Paid = $[?]
Answer (1)
Calculate the total interest rate: 2.0% + 2.1% = 4.1% .
Convert the total interest rate to decimal: 4.1%/100 = 0.041 .
Calculate the annual interest: $450,000 \times 0.041 = $18,450$.
Calculate the interest paid for the 3-month term: $\frac{18,450}{4} = \boxed{$4,612.50}$.
Explanation
Problem Analysis We are given a problem where a business takes out a 3-month loan of $450,000. The interest rate is determined by adding the business risk percentage (2.0%) and the LIBOR rate (2.1%). We need to calculate the total interest paid at the end of the 3-month term.
Calculate Total Interest Rate First, we need to calculate the total interest rate by adding the business risk percentage and the LIBOR rate: T o t a l I n t eres t R a t e = B u s in ess R i s k P erce n t a g e + L I BOR T o t a l I n t eres t R a t e = 2.0% + 2.1% = 4.1%
Convert to Decimal Next, we convert the total interest rate from a percentage to a decimal by dividing by 100: T o t a l I n t eres t R a t e ( d ec ima l ) = 100 T o t a l I n t eres t R a t e T o t a l I n t eres t R a t e ( d ec ima l ) = 100 4.1 = 0.041
Calculate Annual Interest Now, we calculate the annual interest by multiplying the loan amount by the total interest rate (in decimal form): A nn u a l I n t eres t = L o an A m o u n t × T o t a l I n t eres t R a t e ( d ec ima l ) A nn u a l I n t eres t = $450 , 000 × 0.041 = $18 , 450
Calculate Interest Paid Since the loan term is 3 months, which is 1/4 of a year, we divide the annual interest by 4 to find the interest paid for the 3-month term: I n t eres t P ai d = 4 A nn u a l I n t eres t I n t eres t P ai d = 4 $18 , 450 = $4 , 612.50
Final Answer Therefore, the interest paid at the end of the 3-month term is $4,612.50.
Examples
Understanding loan interest calculations is crucial in personal and business finance. For example, if you're planning to buy a car or a house, knowing how interest is calculated helps you determine the actual cost of the loan over time. This understanding enables you to compare different loan offers and make informed financial decisions, ensuring you choose the most favorable terms and avoid unexpected costs. Similarly, businesses use these calculations to manage their debts and investments effectively.
