Question

financial scenario: analyzing a business expansion loan
scenario background:
elena is the owner of a growing bakery and café chain. to expand her business, she plans to open two new locations. she needs a total of $150,000 for renovations, equipment purchases, and initial operating costs. elena is considering a business loan that combines different amounts at various interest rates, allowing her flexibility in repayment terms depending on the loan component.
business expansion loan options:

• loan component a: renovations
• amount: $50,000
• interest rate: 4% per annum
• repayment term: 5 years
• loan component b: equipment purchase
• amount: $70,000
• interest rate: 3.5% per annum
• repayment term: 5 years
• loan component c: operating costs
• amount: $30,000
• interest rate: 5% per annum

what is the weighted average interest rate for elena’s business expansion loan, given the different loan amounts and interest rates?
options: 4.0%, 4.2%, 3.5%, 5.0%

Explanation:

Step1: Calculate total loan amount

Sum the amounts of each loan component: \( 50000 + 70000 + 30000 = 150000 \) (matches the total needed).

Step2: Calculate weighted interest for each component

• Component A: \( 50000 \times 4\% = 50000 \times 0.04 = 2000 \)
• Component B: \( 70000 \times 3.5\% = 70000 \times 0.035 = 2450 \)
• Component C: \( 30000 \times 5\% = 30000 \times 0.05 = 1500 \)

Step3: Sum weighted interests

Total weighted interest: \( 2000 + 2450 + 1500 = 5950 \)

Step4: Calculate weighted average rate

Divide total weighted interest by total loan amount: \( \frac{5950}{150000} \approx 0.039667 \), or \( 3.9667\% \approx 4.0\% \) (rounded appropriately).

Answer:

4.0%