question 1\n3 pts\nalex bought a home treadmill for $1099.00 using his credit card. the sale allows him not…

question 1\n3 pts\nalex bought a home treadmill for $1099.00 using his credit card. the sale allows him not to make payments upto 1 year, but the interest will still accumulated at a rate of 23.5% apr. it will be added to his bill if he does not pay in full balance in 1 year. the interset is componded monthly.\nif alex declded not to make montly payments, what is the payment he has to make in 1 year?\n$

Answer

Explanation:

Step1: Recall compound interest formula

The compound interest formula is $A = P\left(1 + \frac{r}{n}\right)^{nt}$, where:

$A$ is the amount of money accumulated after $n$ years, including interest.
$P$ is the principal amount (the initial amount of money).
$r$ is the annual percentage rate (APR) (decimal).
$n$ is the number of times that interest is compounded per year.
$t$ is the time the money is invested or borrowed for, in years.

Step2: Identify values

$P = 1099.00$ (principal amount)
$r = 23.5% = 0.235$ (annual interest rate in decimal)
$n = 12$ (compounded monthly, so 12 times a year)
$t = 1$ (time in years)

Step3: Substitute values into formula

Substitute the values into the formula: $A = 1099\left(1 + \frac{0.235}{12}\right)^{12\times1}$

Step4: Calculate the exponent and the base

First, calculate $\frac{0.235}{12} \approx 0.0195833$. Then, $1 + 0.0195833 \approx 1.0195833$. The exponent $12\times1 = 12$.

Step5: Calculate the power

Calculate $(1.0195833)^{12}$. Let's compute this: $(1.0195833)^{12} \approx 1.2652$ (using a calculator for the exponentiation)

Step6: Calculate the amount $A$

Now, multiply the principal by this factor: $A = 1099\times1.2652 \approx 1390.45$

Answer:

$$1390.45$ (rounded to the nearest cent)