Answer:
$1545.65.
Step-by-step explanation:
We have been given that Victor has a credit card with an APR of 13.66%, compounded monthly. He currently owes a balance of $1,349.34.
To solve our given problem we will use compound interest formula.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex], where,
A = Final amount after t years,
P = Principal amount,
r = Interest rate in decimal form,
n = Number of times interest is compounded per year,
t = Time in years.
Let us convert our given interest rate in decimal form. [tex]13.66=\frac{13.66}{100}=0.1366[/tex]
Upon substituting our given values in compound interest formula we will get,
[tex]A=1,349.34(1+\frac{0.1366}{12})^{12*1[/tex]
[tex]A=1,349.34(1+0.011383333)^{12[/tex]
[tex]A=1.349.34(1.011383333)[/tex]
[tex]A=1,349.34*1.145485275522[/tex]
[tex]A=1,545.64910167397[/tex] ≈ $[tex]1545.65[/tex]
Therefore, Victor will owe an amount of $1545.65 after one year.
