Victor has a credit card with an APR of 13.66%, compounded monthly. He currently owes a balance of $1,349.34. Assuming that Victor makes no purchases or payments, how much will he owe after one year, to the nearest cent?
A = P (1 + r/n)^nt
A = 1,349.34(1+0.1366/12)^12
A = 1545.65
answer: he will owe $1545.65 after one year
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.
\(A=P(1+\frac{r}{n})^{nt}\), 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.
\(13.66\%=\frac{13.66}{100}=0.1366\)
Upon substituting our given values in compound interest formula we will get,
\(A=\$1,349.34(1+\frac{0.1366}{12})^{12*1}\)
\(A=\$1,349.34(1+0.011383333)^{12}\)
\(A=\$1,349.34(1.011383333)^{12}\)
\(A=\$1,349.34*1.145485275522\)
\(A=\$1,545.64910167397\approx \$1545.65\)
Therefore, Victor will owe an amount of $1545.65 after one year.