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Leviafan [203]
2 years ago
14

You purchased a new car. The car had a list price of $41,070. You are paying 5.09% interest compounded monthly over a payment pe

riod of FIVE years. If you also had to pay 5.86% sales tax, a $384 vehicle registration fee, and an $89 documentation fee, what is your monthly payment?
Mathematics
1 answer:
Mashutka [201]2 years ago
4 0

Answer:

The monthly payment is approximately $2,356.89

Step-by-step explanation:

The list price of the car, P = $41,070

The interest rate payed, r = 5.09% compounded monthly

Therefore, the number of interest calculated per period, n = 1

The payment period, t = 5 years

The amount payed as sales tax = 5.86%

The amount paid as registration fee = $384

The amount paid as documentation fee = $89

The total amount to be paid, A = 41,070 + 41,070 × 0.0586 + 384 + 89 = 43,949.702

Therefore, the monthly payment, 'M', is given by the following formula;

M = \dfrac{P \cdot \left(\dfrac{r}{n} \right) \cdot \left(1+\dfrac{r}{n} \right)^{n  \cdot t} }{\left(1+\dfrac{r}{n } \right)^{n  \cdot t} - 1}

Therefore, we get;

M = \dfrac{43,949.702\times \left(\dfrac{0.0509}{1} \right) \cdot \left(1+\dfrac{0.0509}{1} \right)^{1  \times 60} }{\left(1+\dfrac{0.0509}{1 } \right)^{1  \times 60} - 1} \approx 2,356.89

The monthly payment, M ≈ $2,356.89.

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At the null hypothesis, it is <u>tested if the consumption is not different</u>, that is, if the subtraction of the means is 0, hence:

H_0: \mu_1 - \mu_2 = 0

At the alternative hypothesis, it is <u>tested if the consumption is different</u>, that is, if the subtraction of the means is not 0, hence:

H_1: \mu_1 - \mu_2 \neq 0

Two groups of 22 patients, hence, the standard errors are:

s_1 = \frac{45.1}{\sqrt{22}} = 9.6154

s_2 = \frac{26.4}{\sqrt{22}} = 5.6285

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t = \frac{25 - 0}{11.14}

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The p-value of the test is found using a <u>two-tailed test</u>, as we are testing if the mean is different of a value, with <u>t = 2.2438</u> and 22 + 22 - 2 = <u>42 df.</u>

  • Using a t-distribution calculator, this p-value is of 0.0302.

Since the p-value of the test is of 0.0302, which is <u>less than the standard significance level of 0.05</u>, the data provides convincing evidence that the average food intake is different for the patients in the treatment group.

A similar problem is given at brainly.com/question/25600813

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