To calculate the amount to be paid back after 3 years on a credit card loan with an initial principal amount of $3000 and an interest rate of 15% compounded yearly, you can use the formula for compound interest:
\[ A = P(1 + r)^t \]
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).
- \(t\) is the number of years the money is invested or borrowed.
In this case:
- \(P = 3000\)
- \(r = 0.15\) (15% as a decimal)
- \(t = 3\)
Plugging in the values:
\[ A = 3000(1 + 0.15)^3 \]
Now calculate \(1 + 0.15\):
\[ 1 + 0.15 = 1.15 \]
Now raise it to the power of 3:
\[ 1.15^3 \approx 1.520875 \]
Now multiply this by the principal amount:
\[ A \approx 3000 \times 1.520875 \approx 4562.63 \]
Thus, the amount to be paid back after 3 years on a $3000 credit card loan with a 15% interest rate compounded yearly is approximately $4562.63.