If your deposit of $20 000 becomes $20 523 at the end of 180 days, what is the annual yield earned?

Question

If your deposit of $20 000 becomes $20 523 at the end of 180 days, what is the annual yield earned?

BlackTom AI · Accepted Answer

To evaluate the annual yield, we start from the actual interest earned and the time period involved.
Option 1: 5.10% — This would correspond to a slightly smaller annualized rate. If you compute the 180-day gain of 523 on a 20000 principal, you get 523/20000 = 0.02615 for half a year. Annualizing with a 365-day year gives 0.02615 × (365/180) ≈ 0.0530, i.e., 5.30%. Thus 5.10% understates the correct annualization.
Option 2: 5.23% — This matches the 360-day convention, where the factor is 365/360 ≈ 1.01389. Using 0.02615 × (365/180) yields about 0.0530 (5.30%), while 0.02615 × 2 (for a simple 180-day doubling) would be 0.0523 (5.23%). If we were strictly using a 360-day year, 5.23% could appear plausible, but the problem specifies annual yield in a context that aligns with 365 days, making this slightly off.
Option 3: 5.17% — This is another underestimate when using the precise 365-day annualization factor. The correct 365-day annualization of 0.02615 for 180 days gives roughly 0.0530, not 0.0517.
Option 4: 5.30% — This is the highest-precision result when the 365-day year is used for annualization: 523/20000 = 0.02615 for 180 days, and 0.02615 × (365/180) ≈ 0.0530, i.e., 5.30%. Therefore this option aligns with the standard 365-day annual yield calculation.

If your deposit of $20 000 becomes $20 523 at the end of 180 days, what is the annual yield earned?单项选择题

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