To calculate the amount to be paid back after three years on a $3,000 credit card loan with an interest rate of 15% compounded yearly, we can use the formula for compound interest:
\[ A = P (1 + r)^n \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial sum of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of years the money is invested or borrowed.
In this case:
- \( P = 3000 \)
- \( r = 0.15 \) (15% expressed as a decimal)
- \( n = 3 \)
Now substitute the values into the formula:
\[ A = 3000 \times (1 + 0.15)^3 \]
\[ A = 3000 \times (1.15)^3 \]
Calculating \( (1.15)^3 \):
\[ (1.15)^3 \approx 1.520875 \]
Now, substitute this back into the formula:
\[ A \approx 3000 \times 1.520875 \approx 4562.63 \]
Therefore, the amount to be paid back after three years is approximately $4,562.63.
So the correct response is:
$4,562.63
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