Question
A college receives a donation of $955,000 that earns 5.33% interest compounded daily. How much interest would the college earn in one year?
Scr
2024-
ScI
2024-
2
3
Sc
2024-
$50,901.50
$1,007,278.53
$52,278.53
$1,005,901.50
Scr
2024-
ScI
2024-
2
3
Sc
2024-
$50,901.50
$1,007,278.53
$52,278.53
$1,005,901.50
Answers
GPT-4o mini
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.
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
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.