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

$267,572.61
$267,572.61

$4,562.63
$4,562.63

$3,138.08
$3,138.08

$4,271.48
$4,271.48

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 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:

1. Calculate \( 1 + r \):

\[
1 + 0.15 = 1.15
\]

2. Raise that to the power of \( n \):

\[
1.15^3 \approx 1.520875
\]

3. 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**