Question

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. (1 point)
Responses

$4,562.63
$4,562.63

$4,271.48
$4,271.48

$3,138.08
$3,138.08

$267,572.61

Answer 1

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**