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Find the interest earned (bank discount), purchase price, and effective rate of interest for a $2,500,000,...

23. Find the interest earned (bank discount), purchase price, and effective rate of interest for a $2,500,000, 39-week T-bill with a discount rate of 6.5%. What is the effective rate of interest to the nearest tenth?
☐ 7.0%
☐ 7.2%
☐ 6.8%
☐ 6.6%

Answer

Interest Earned (Bank Discount): The bank discount is calculated as follows:

Discount = Face Value × Discount Rate × (Days to Maturity / 360)

Discount = $2,500,000 × 0.065 × (273 / 360) = $123,958.33

Purchase Price: The purchase price is the face value minus the discount:

Purchase Price = Face Value - Discount = $2,500,000 - $123,958.33 = $2,376,041.67

Effective Rate of Interest: The effective rate of interest is calculated as follows:

Effective Rate = (Discount / Purchase Price) × (360 / Days to Maturity)

Effective Rate = ($123,958.33 / $2,376,041.67) × (360 / 273) = 0.068 or 6.8%

Answer: 6.8%

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