Find the area of the circle. Write your solution in terms of and round to the nearest hundredth.

Mathematics

1 answer:

sleet_krkn [62]2 years ago

4 0

Answer:

A = 25π cm²

In decomal form = 78.5cm²

Step-by-step explanation:

Area of a circle is expressed as;

A = πr²

r is the radius of the circle

Since we are not given the radius. Let us assume that r = 5cm

Substitute into the formula;

A = π(5)²

A = 25π cm²

As a decomal;

A = π(5)²

A = 3.14 * 25

A = 78.5cm²

Note that the radius of the circle was assumed. The same calculation can be employed for any value of the radius

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Step-by-step explanation:

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2 years ago

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 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

Given that he earns a gross annual income of $64,570 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

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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 = $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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