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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.
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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).
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.
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.