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3 years ago

Emma decides to invest $990,000 in a period annuity that earns a 2.2% APR,

Mathematics

2 answers:

iris [78.8K]3 years ago

8 0

The correct answer is D. 3759.04

Explain

The formula is

PMT= amount {APR/n/(1+APR/n)^ny-1

APR is rate per year

N - is number of month

Y- number of year

Now let me begin ...

amount = 990,000
APR= 2.2%
N=12
Y= 20 yrs

Now let’s put all this in the formula and simplify

Pmt = 990000{2.2/12/(1+2.2/12)^12x20-1

Now simply

Pmt= 990000{0.18333/(1+0.18333)^240 -1

990000{0.18333/(1.18333)^240 -1}

1.00183333^240 -1= 0.55208

Pmt = 990000x 0.00183333/0.55208

1814.9967/0.55208

= 3759.04

Sorry for taking long , I have to check my work twice before sending , so I can give you correct answer

I hope this help you :D

Pani-rosa [81]3 years ago

4 0

Answer: B) 6462.32

Step-by-step explanation:

Compound interest can be calculated via the attachment.

Hope it helps <3

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The first two terms in an arithmetic progression are -2 and 5. The last term in the progression is the only number in the progre

Rudik [331]

Given:

The first two terms in an arithmetic progression are -2 and 5.

The last term in the progression is the only number in the progression that is greater than 200.

To find:

The sum of all the terms in the progression.

Solution:

We have,

First term : $a=-2$

Common difference : $d = 5 - (-2)$

$= 5 + 2$

$= 7$

nth term of an A.P. is

$a_n=a+(n-1)d$

where, a is first term and d is common difference.

$a_n=-2+(n-1)(7)$

According to the equation, $a_n>200$ .

$-2+(n-1)(7)>200$

$(n-1)(7)>200+2$

$(n-1)(7)>202$

Divide both sides by 7.

$(n-1)>28.857$

Add 1 on both sides.

$n>29.857$

So, least possible integer value is 30. It means, A.P. has 30 term.

Sum of n terms of an A.P. is

$S_n=\dfrac{n}{2}[2a+(n-1)d]$

Substituting n=30, a=-2 and d=7, we get

$S_{30}=\dfrac{30}{2}[2(-2)+(30-1)7]$

$S_{30}=15[-4+(29)7]$

$S_{30}=15[-4+203]$

$S_{30}=15(199)$

$S_{30}=2985$

Therefore, the sum of all the terms in the progression is 2985.

6 0

3 years ago

Solve for C:<br> Spam: deiodhwidweiudjegydjwe

Maksim231197 [3]

Answer:

$C=\frac{5F-160}{9}$

Step-by-step explanation:

Let's solve for C.

$F=\frac{9C}{5}$

Step 1: Flip the equation.

$\frac{9}{5} C+32=F$

Step 2: Add $-32$ to both sides.

$\frac{9}{5} C+32+-32=F+-32$

$\frac{9}{5}C=F-32$

Step 3: Divide both sides by $\frac{9}{5}$ .

$\frac{\frac{9}{5}C}{\frac {9} {5}}=\frac{F-32}{\frac{9}{5} }$

$C=\frac{5F-160}{9}$

Answer:

$C=\frac{F-160}{9}$

8 0

2 years ago

If ln(4x+y)=2x-3,then dy/dx=

Viktor [21]

$\ln(4x+y)=2x-3$

Differentiate both sides wrt $x$ :

$\dfrac{\mathrm d(\ln(4x+y))}{\mathrm dx}=\dfrac{\mathrm d(2x-3)}{\mathrm dx}$

By the chain rule, we get

$\dfrac1{4x+y}\dfrac{\mathrm d(4x+y)}{\mathrm dx}=2$

$\dfrac{4+\frac{\mathrm dy}{\mathrm dx}}{4x+y}=2$

Solve for $\frac{\mathrm dy}{\mathrm dx}$ :

$4+\dfrac{\mathrm dy}{\mathrm dx}=8x+2y$

$\boxed{\dfrac{\mathrm dy}{\mathrm dx}=8x+2y-4}$

4 0

2 years ago

Simplify. (-7y^2+4y+9)+(6y^2-5y+9)-(2y^2-9y-2)

Natali5045456 [20]

Combine like terms

-7y² + 6y² - 2y² = -3y²

4y + (-5y) - (-9y) = 4y - 5y + 9y = 8y

9 + 9 - (-2) = 9 + 9 + 2 = 20

-3y² + 8y + 20 is your answer

hope this helps

7 0

3 years ago

A research company desires to know the mean consumption of meat per week among people over age 40. A sample of 610 people over a

Papessa [141]

Answer: $(3.0,\ 3.2)$

Step-by-step explanation:

Confidence interval for population mean is given by :-

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$ (1)

, where $\overline{x}$ = Sample mean

$z_{\alpha/2}$ = Critical z-value

$\sigma$ = Population standard deviation.

n= Sample size.

As per given , we have

n= 610

$\sigma=1.1$

$\overline{x}=3.1$

Significance level for 85% confidence : $\alpha=1-0.85=0.15$

By z-table critical two tailed z-value : $z_{\alpha/2}=z_{0.075}=1.44$

Put all values in (1) , we get

$3.1\pm 1.44\dfrac{1.1}{\sqrt{610}}$

$3.1\pm 1.44\dfrac{1.1}{24.698}$

$3.1\pm 0.064$

$=(3.1-0.064,\ 3.1+0.064)=(3.036,\ 3.164)\approx(3.0,\ 3.2)$

Hence, the 85% confidence interval for the mean consumption of meat among people over age 40. = $(3.0,\ 3.2)$

5 0

3 years ago