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Dafna11 [192]
3 years ago
15

Tom Burke buys a home in Virginia for $139,000. He puts down 30% and obtains a mortgage for 25 years at 12%. The portion of the

first payment that covers interest is:
Mathematics
2 answers:
Marat540 [252]3 years ago
7 0
You didn't specify the periodic payment in your question. I will solve it assuming that payment is made monthly.

Amount owing by Tom = 70% of 139,000 = 0.7 x 139,000 = $97,300

Present Value of an annuity is given by PV = P(1 - (1 + r)^-n)/r; where P is the periodic (monthly) payment, r is the interest rate = 12%/12 = 1% = 0.01, n is the number of periods = 25 x 12 = 300 months.

97,300 = P(1 - (1 + 0.01)^-300)/0.01
P = 973/(1 - (1.01)^-300) = 973/(1 - 0.050534) = 1,024.79
Thus Tom pays $1,024.79 per month.

Interest due for the first month = 0.01 x 97,300 = $973

Therefore, the portion of the first payment that covers the interest is $973
SVEN [57.7K]3 years ago
3 0

Answer:

$973.00

Step-by-step explanation:

$139,000 x .70 = $97,300/$1,000 = $97.3 x $10.54 = $1,025.54

$97,300 x .12 x 1/12 = $973.00

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The angle from horizontal to the point where you stopped your head is called the angle of depression.

From a hot-air balloon, Brody measures a 39° angle of depression to a landmark that's 532 feet away, measuring horizontally.

The angle of depression = 39°

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An advertising executive claims that there is a difference in the mean household income for credit cardholders of Visa Gold and
Maslowich

Answer:

Null hypothesis:\mu_{Visa}=\mu_{Mastercard}

Alternative hypothesis:\mu_{Visa} \neq \mu_{Mastercard}

t=\frac{66970-59060}{\sqrt{\frac{9500^2}{11}+\frac{10000^2}{17}}}}=2.108  

p_v =2*P(t_{26}>2.108)=0.0448

Comparing the p value with the significance level given \alpha=0.1 we see that p_v so we can conclude that we can reject the null hypothesis, and a would be a significant difference between the  in the mean household income for credit cardholders of Visa Gold and of MasterCard Gold at 10% of significance .

Step-by-step explanation:

Data given and notation

\bar X_{Visa}=66970 represent the mean for Visa

\bar X_{Mastercard}=59060 represent the mean for the sample Mastercard

s_{Visa}=9500 represent the population standard deviation for Visa

s_{Mastercard}=10000 represent the population standard deviation for Mastercard

n_{Visa}=11 sample size for the group Visa

n_{Mastercard}=17 sample size for the group Mastercard

t would represent the statistic (variable of interest)

\alpha=0.1 significance level provided

Develop the null and alternative hypotheses for this study?

We need to conduct a hypothesis in order to check if the means for the two groups are different, the system of hypothesis would be:

Null hypothesis:\mu_{Visa}=\mu_{Mastercard}

Alternative hypothesis:\mu_{Visa} \neq \mu_{Mastercard}

Since we don't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:

z=\frac{\bar X_{Visa}-\bar X_{Masterdcard}}{\sqrt{\frac{s^2_{Visa}}{n_{Visa}}+\frac{s^2_{Mastercard}}{n_{Mastercard}}}} (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the value of the test statistic for this hypothesis testing.

Since we have all the values we can replace in formula (1) like this:

t=\frac{66970-59060}{\sqrt{\frac{9500^2}{11}+\frac{10000^2}{17}}}}=2.108  

What is the p-value for this hypothesis test?

First we need to calculate the degrees of freedom given by:

df= n_{Visa}+n_{Mastercard}-2 = 11+17-2= 26

Since is a bilateral test the p value would be:

p_v =2*P(t_{26}>2.108)=0.0448

Based on the p-value, what is your conclusion?

Comparing the p value with the significance level given \alpha=0.1 we see that p_v so we can conclude that we can reject the null hypothesis, and a would be a significant difference between the  in the mean household income for credit cardholders of Visa Gold and of MasterCard Gold at 10% of significance .

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