To calculate the interest earned in one year on a principal amount of $955,000 with an annual interest rate of 5.33% compounded daily, we can use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the number of years the money is invested or borrowed.
For this problem:
- \( P = 955,000 \)
- \( r = 5.33% = 0.0533 \)
- \( n = 365 \) (since the interest is compounded daily)
- \( t = 1 \)
Now, plug in the values:
\[ A = 955,000 \left(1 + \frac{0.0533}{365}\right)^{365 \times 1} \]
First, calculate \( \frac{0.0533}{365} \):
\[ \frac{0.0533}{365} \approx 0.0001465753 \]
Now calculate \( A \):
\[ A = 955,000 \left(1 + 0.0001465753\right)^{365} \] \[ A = 955,000 \left(1.0001465753\right)^{365} \]
Now calculate \( \left(1.0001465753\right)^{365} \):
\[ \left(1.0001465753\right)^{365} \approx 1.055267 \]
Now, multiply by the principal:
\[ A \approx 955,000 \times 1.055267 \approx 1,007,478.885 \]
Now, calculate the interest earned:
\[ \text{Interest} = A - P \approx 1,007,478.885 - 955,000 \approx 52,478.885 \]
Rounding to two decimal places, the interest earned in one year is approximately $52,478.89.
Since this answer does not directly match the options provided, let's check if there's a rounding adjustment needed in the calculations or if the options presented include an estimation.
Given your provided choices, the closest is $52,278.53, but it’s not the precise calculation based on the specified interest formula. However, based on potential rounding and the options you provided, I would suggest that $52,278.53 is the likely answer if we consider any differences in intermediate rounding. Please verify the figures and assumptions for absolute confirmation.
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