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  3. a credit union lends 5m in home loans (with durati

A credit union lends 5m in home loans (with duration of 12.8242 years) and 5m...

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Accounting

A credit union lends 5m in home loans (with duration of 12.8242 years) and 5m in small business loans (with duration of 8.4847 years). It finances 90% of its lending with deposits (with duration of 4.7623 years). Moreover, the credit union has an additional 1m invested in money market instruments with duration zero. What is the duration of the credit union's balance sheet (in years)?

***I've tried to make these quantities somewhat realistic. First of all, credit unions (like all banks), face capital requirements. 10% is roughly the amount of equity capital credit unions need to maintain. Credit unions also prefer high-quality borrowers, so when computing duration, I've assumed that our credit union lends at "prime" rates. I've assumed that the home loans are 250k USD, 30-year 3% fixed and small business loans are 1m USD, 20-year 4.75% fixed (roughly the prime rate). Both loans are compounded monthly and are fully amortizing (unlike a bond, the future value is zero). Current 5-year CD rates are roughly 2% compounded monthly and non-amortizing. ***

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