Respuesta :
Answer:
A. $7.17
Step-by-step explanation:
We have been given that a mechanic uses his credit card to pay for a compressor that costs $477.95 and does not pay on it until the second month.
We will use compound interest formula to solve our given problem.
[tex]A=P(1+\frac{r}{n})^{nT}[/tex] where,
A = Final amount after T years,
P = Principal amount,
r = Annual interest rate in decimal form,
n = Periods of compounding,
T = Time in years.
Let us multiply our given rate by 12 to get APR and convert it in decimal form.
[tex]APR=12\times 1.5\%[/tex]
[tex]APR=18\%[/tex]
[tex]18\%=\frac{18}{100}=0.18[/tex]
Since 1 year equals 12 months, so 1 month will be 1/12 year.
Upon substituting our given values in above formula we will get,
[tex]A=477.95(1+\frac{0.18}{12})^{12\times\frac{1}{12}}[/tex]
[tex]A=477.95(1+0.015)^{1}[/tex]
[tex]A=477.95(1.015)[/tex]
[tex]A=485.11925[/tex]
Now let us subtract principal amount from the final amount to get the monthly interest charge at the end of 1st month.
[tex]\text{The monthly interest charge be at the end of the first month}=485.11925-477.95[/tex]
[tex]\text{The monthly interest charge be at the end of the first month}=7.16925\approx 7.17[/tex]
Therefore, the monthly interest charge be at the end of the first month will be $7.17 and option A is the correct choice.
