Calculate the amount to be paid back after two years on a $5,000 credit card loan with an interest rate of 20% compounded yearly.(1 point)

Question

Responses

$7,200
$7,200 - no response given

$8,042.19
$8,042.19 - incorrect

$5,204.88
$5,204.88 - no response given

$7,000

Answer 1

To calculate the amount to be paid back after two years on a $5,000 credit card loan with an interest rate of 20% 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 amount of money, in this case, $5,000).
• $r$ is the annual interest rate (decimal, so 20% becomes 0.20).
• $n$ is the number of years the money is invested or borrowed (in this case, 2 years).

Substituting the values, we get:

$$A=5000(1+0.20{)}^2$$

$$A=5000(1.20{)}^2$$

$$A=5000(1.44)$$

$$A=7200$$

Therefore, the amount to be paid back after two years is $7,200.