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2 years ago

Mr. Steiner purchased a car for about $14,000. Assuming his loan was

Mathematics

1 answer:

djverab [1.8K]2 years ago

5 0

Answer:

$415.18

Explanation:

The calculation of the present value of a cash flow or other income stream that produces $1 in income over so many periods of time.

DATA

Amount borrowed = $12,500

Annual interest rate = 12.00%

Monthly interest rate = 1.00%

Period = 36 months

Let monthly payment be x

12,500 = x/1.01 + x/1.01^2 + x/1.01^3 … + x/1.01^35 + x/1.01^36

12,500 = x * (1 - (1/1.01)^36) / 0.01

12,500 = x * 30.107505

x = 12,500/30.107505

x = 415.18

The monthly payment is $415.18

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Haley has deposited $816 in a savings account that earns interest at a rate of 2.9% compounded daily. what will the account bala

Marrrta [24]

The answer is $1,059.34

Explanation:

The formula for compound interest is

I = P(1+ $\frac{r}{n}$ $)^{nt}$

Where I = interest, P = principal (original deposit), r = interest rate, n = number of times compounded per year, and t = time, in years.

Using this formula, we can substitute the information from the question for the their corresponding variables.

Now, after filling in the information, your formula should look like this

I = 816(1+ $\frac{0.029}{365}$ $)^{365*9}$

*The reason that the rate is 0.029 instead of 2.9 is that 2.9 is a percent, and we need a decimal. To convert it, you just need to divide the percent by 100.

Now, all we need to do is solve the equation using order of operations (PEMDAS).

I will divide the 0.029 by 365 first.

I = 816(1+0.00008 $)^{365*9}$

**This is not the exact decimal. It would be too difficult to write entirely, but I will be using the true decimal in my calculations.

Next, we have to add 1 to the decimal.

I = 816(1.00008 $)^{365*9}$

Now, I will multiply 365 and 9 together.

I = 816(1.00008 $)^{3285}$

Next, we must raise the number within the parenthesis to the power of 3285.

I = 816(1.3)

***Again, this is not the actual decimal. The real one will be used in the calculation, though, like before.

Finally, we have to multiply the decimal by the principal, 816.

I = $1,059.34

7 0

3 years ago

Simplify the expression.

Artyom0805 [142]

Your answer should be (w-1 over 1.5v)-1

8 0

3 years ago

Find the volume of the given solid. Bounded by the cylinder y2 + z2 = 16 and the planes x = 2y, x = 0, z = 0 in the first octant

erastovalidia [21]

Answer:

$\mathbf{ \dfrac{128}{3}}$

Step-by-step explanation:

Given that:

$y^2 + z^2 = 16; \\ \\ where; \ x = 2y , x =0, z= 0$

$Replace \ z = 0 \ \text{in the given equation ;} y^2+z^2=16$

$Then;$

$y^2 = 16 \\ \\ y = \sqrt{16} \\ \\ y = \pm 4$

$\text{So; in 1st octant \ limits of y }= 0 \to 4 \ \text{and for x }= 0 \to 2y$

∴

$\text{Volume of solid: (V) = }\int ^{4}_{y=0} \int ^{2y}_{x=0} \sqrt{16-y^2} \ dxdy \\ \\ = \int^4_{y=0} \sqrt{16 -y^2} \ (x)^{2y} _o \ dy \\ \\ = \int^4_{y=0}\sqrt{16 -y^2} (2y -0) \ dy \\ \\ V = \int^{4}_{y=0} \ 2y \sqrt{16 - y^2} \ dy$

$Now, let:\\\\ 16 - y^2 = u \\ \\ -2ydy = du \\ \\ 2ydy = -du \\ \\ Hence, when \ y = 0; u = 16 \\ \\ and \\ \\ when \ y = 4 \ then \ u = 0$

∴

$V = \int ^4 _{y=0} \ 2y \sqrt{16 -y^2 } \ dy \\ \\ = \int ^0_{16} - \sqrt{u}\ du \\ \\ = - \int^0_{16} \ u^{^{\dfrac{1}{2}}} \ du \\ \\ = \Bigg [\dfrac{u^{^{\dfrac{1}{2}+1}}}{\dfrac{1}{2}+1 } \Bigg]^0_{16} \\ \\ =\Bigg[ -\dfrac{u^{\dfrac{3}{2}}}{\dfrac{3}{2}}^0_{16} \Bigg] \\ \\$

$= - \dfrac{2}{3}\Big( u^{\dfrac{3}{2}}\Big)^0_{16} \\ \\ = - \dfrac{2}{3} \Big(0^{^\dfrac{3}{2}}}- 16^{^{\dfrac{3}{2}}}\Big ) \\ \\ = - \dfrac{2}{3} \Big(0 - (4^2)^{^{\dfrac{3}{2}}}\Big ) \\ \\ = - \dfrac{2}{3} \Big(-(4)^{3}}\Big )$