cassie is financing a $2,400 treadmill. she is going to use her credit card for the purchase. her card…

cassie is financing a $2,400 treadmill. she is going to use her credit card for the purchase. her card charges 17.5% interest compounded monthly. she is not required to make minimum monthly payments. answer parts a through c below.\na. how much will cassie pay in interest if she waits a full year before paying the full balance?\n$ (round to the nearest cent as needed.)

cassie is financing a $2,400 treadmill. she is going to use her credit card for the purchase. her card charges 17.5% interest compounded monthly. she is not required to make minimum monthly payments. answer parts a through c below.\na. how much will cassie pay in interest if she waits a full year before paying the full balance?\n$ (round to the nearest cent as needed.)

Answer

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. Here, $P=$2400$, $r = 0.175$ (since $17.5%=0.175$), $n = 12$ (compounded monthly), and $t = 1$.

Step2: Calculate the amount owed after 1 year

$A=2400(1 +\frac{0.175}{12})^{12\times1}$ First, calculate the value inside the parentheses: $\frac{0.175}{12}\approx0.0145833$, then $1+\frac{0.175}{12}=1 + 0.0145833=1.0145833$. Next, raise it to the 12th power: $(1.0145833)^{12}\approx1.19094$. Then, $A = 2400\times1.19094=$2858.256$.

Step3: Calculate the interest

The interest $I$ is the difference between the amount owed $A$ and the principal $P$. So, $I=A - P$. $I=2858.256−2400=$458.256\approx$458.26$.

Answer:

$458.26$