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 to be paid back,
- \( P \) is the principal amount (the initial loan amount),
- \( r \) is the annual interest rate (as a decimal),
- \( n \) is the number of years the money is borrowed for.
Given:
- \( P = 3000 \)
- \( r = 0.15 \) (15% as a decimal)
- \( n = 3 \)
Plugging in the values:
\[ A = 3000(1 + 0.15)^3 \]
Now, we calculate it step by step:
- Calculate \( 1 + r \):
\[ 1 + 0.15 = 1.15 \]
- Raise that to the power of \( n \):
\[ 1.15^3 \approx 1.520875 \]
- Multiply by the principal:
\[ A = 3000 \times 1.520875 \approx 4562.63 \]
Thus, the amount to be paid back after three years is approximately $4,562.63.
Therefore, the correct answer is:
$4,562.63
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