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Answer:
5.827%
Step-by-step explanation:
Interest compounded annually, and interest compounded continuously will have the same effective rate if the annual multipliers are the same. For the interest multipliers to be the same, you must have ...
1 +6% = e^r
ln(1.06) = r ≈ 0.0582689 ≈ 5.827%
The competing bank should offer a rate of 5.827% compounded continuously.