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Calculate T-Bill Investment Rate of Return: $25,000 Face Value Bought for $24,650
Mathematics (Finance)
High School Grade 12 / College Introductory Finance
Question Content
Maxwell purchased $25,000 worth of 52-week T-Bills for $24,650. What will be the rate of return on his investment? (Round your answer to two decimal places.)
Correct Answer
1.42%
Detailed Solution Steps
1
Step 1: Calculate the profit from the T-Bill investment. Profit = Face Value - Purchase Price = $25,000 - $24,650 = $350.
2
Step 2: Use the simple rate of return formula: Rate of Return = (Profit / Purchase Price) × 100%.
3
Step 3: Substitute the values: Rate of Return = ($350 / $24,650) × 100% ≈ 0.014199 × 100% = 1.42% when rounded to two decimal places.
Knowledge Points Involved
1
Treasury Bill (T-Bill) Rate of Return
T-Bills are zero-coupon securities, so their rate of return is calculated as the percentage gain from the difference between the face value (paid at maturity) and the discounted purchase price. The formula is (Face Value - Purchase Price)/Purchase Price × 100%, used for short-term (1-year or less) government securities.
2
Simple Rate of Return
A basic metric to calculate the percentage gain or loss on an investment over a period, calculated as (Net Profit / Initial Investment) × 100%. It is used for simple, single-period investments with no compounding.
3
Rounding Decimal Places for Financial Calculations
In finance, percentages are typically rounded to two decimal places to represent basis points (1 basis point = 0.01%), ensuring precision for investment reporting and analysis.
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