To calculate the total amount and interest earned on a principal amount with compound interest, you can use the formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
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.
Given:
- \( P = 675 \)
- \( r = 0.03 \) (3% expressed as a decimal)
- \( n = 4 \) (compounded quarterly)
- \( t = 6 \)
Now plugging in the values:
\[ A = 675 \left(1 + \frac{0.03}{4}\right)^{4 \times 6} \]
First, calculate \( \frac{0.03}{4} \):
\[ \frac{0.03}{4} = 0.0075 \]
Now substitute back into the formula:
\[ A = 675 \left(1 + 0.0075\right)^{24} \] \[ A = 675 \left(1.0075\right)^{24} \]
Now calculate \( (1.0075)^{24} \):
\[ (1.0075)^{24} \approx 1.191505 \]
Now calculate \( A \):
\[ A \approx 675 \times 1.191505 \approx 803.26 \]
To find the interest earned, subtract the principal from the total amount:
\[ \text{Interest} = A - P = 803.26 - 675 \approx 128.26 \]
The closest option provided is:
- $130.99
Therefore, the correct answer is approximately $130.99.
1 answer