Question
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)
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
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
Answers
GPT-4o mini
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**.
\[
A = P(1 + r)^n
\]
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**.