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A lender is calculating the expected payoff from a risky loan. Match each mathematical component of the calculation with its correct conceptual description. In these expressions, 'L' is the loan principal and 'r' is the interest rate.
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A microfinance institution is considering two different loan applications, each for $5,000.
- Loan Alpha offers a 15% interest rate, but the borrower has a profile that suggests an 85% probability of full repayment.
- Loan Beta offers a 10% interest rate, and this borrower's profile suggests a 95% probability of full repayment.
Assuming the institution's primary goal is to maximize its expected monetary return, which loan should it approve and why?
Break-Even Analysis for a Risky Loan
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A bank is considering two potential loan structures for a $1,000 principal amount. The bank's expected payoff will be identical whether it offers the loan with a 20% interest rate and an 80% probability of repayment, or with a 10% interest rate and a 90% probability of repayment.
A commercial bank lends $20,000 to a startup at an 8% interest rate. The bank assesses the probability of full repayment to be 90%. The bank's expected payoff from this loan is $____. (Please provide your answer as a whole number without currency symbols or commas).
Evaluating Lending Strategies
A financial analyst is calculating a lender's expected payoff from a loan where there is a risk of default. Arrange the following steps into the correct logical sequence for this calculation.
A financial institution offers a $20,000 loan at a 10% interest rate, with an initial assessment that the borrower has a 95% probability of full repayment. After a new credit report becomes available, the institution revises the probability of repayment down to 90%. To achieve the exact same expected monetary payoff as under the initial assessment, what new interest rate must the institution charge?
Strategic Loan Adjustment
A bank is considering two potential loan structures for a $1,000 principal amount. The bank's expected payoff will be identical whether it offers the loan with a 20% interest rate and an 80% probability of repayment, or with a 10% interest rate and a 90% probability of repayment.
Lender's Break-Even Condition for a Risky Loan