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balandron [24]
3 years ago
7

A right triangle has side lengths d, e, and f as shown below.

Mathematics
1 answer:
Katena32 [7]3 years ago
5 0

Answer:

tanx=d/f, sinx=d/e, cosx=f/e

Step-by-step explanation:

Find the opposite, Adjacent and hypotenuse of the right triangle.

Opposite= d , Adjacent= f, Hypotenuse= e

Tanx = opposite/adjacent

Sinx= opposite/hypotenuse

Cosx= adcajent/hypotenuse

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Victor earns a gross annual income of $64,570 and is buying a home for $125,340. He is making a 15% down payment and financing t
Oliga [24]
Part A:

Given that <span>Victor is buying a home for $125,340 and that he is making a 15% down payment.

The amount of down payment is given by 15% of $125,340 = 0.15 x $125,340 = $18,801.

Therefore, the amount of mortgage he needs to borrow is given by $125,340 - $18,801 = $106,539


Part B

</span>Given that he earns a gross annual income of $64,570 <span>and that the loan of $106,539 will be spread for 20 years at 3.75% interest.

$106,539 / 20 = $5,326.95

Roughly he will be paying about $5,000 every year which is way below his annual gross income. 

Therefore, he can afford the mortgage.


Part C

The monthly mortgage payment can be calculated using the present value of annuity formula given by

</span>PV=P\left( \frac{1-\left(1+\left( \frac{r}{t} \right)\right)^{-nt}}{ \frac{r}{t} } \right)
<span>
where: PV is the current value of the loan, P is the periodic (monthly) payment, r is the annual interest rate, t is the number of payment in one year and n is the number of years.

Here, PV = </span>$106,539; r = 3.75% = 0.0375; t is 12 payments in one year (since payment is to be made monthly); n = 20 years.

Thus, we have:

106,539=P\left( \frac{1-\left(1+\left( \frac{0.0375}{12} \right)\right)^{-20\times12}}{ \frac{0.0375}{12} } \right) \\  \\ =P\left( \frac{1-\left(1+0.003125\right)^{-240}}{0.003125} \right)=P\left( \frac{1-\left(1.003125\right)^{-240}}{0.003125} \right) \\  \\ =P\left( \frac{1-0.472919}{0.003125} \right)=P\left( \frac{0.527081}{0.003125} \right)=168.666P \\  \\ \Rightarrow P= \frac{106,539}{168.666} =631.66

Therefore, the monthly mortgage payment is $631.66


Part D

Since he will make a monthly payment of $631.66 for 20 years, thus he will make a total of $631.66 x 12 x 20 = $151,598.40

Therefore, his total payment for the house will be $151,598.40


Part E

Since he will make a total payment of $151,598.40 for a mortgage loan of $106,539.

Therefore, the amount of interest he will pay is given by $151,598.40 - $106,539 = $45,059.40
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Step-by-step explanation:

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Answer:

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