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Hitman42 [59]
3 years ago
15

You paid $44 to a loan company for the use of $1,153 for 119 days, what annual rate of interest did they charge? (Assume a 360-d

ay year.) If The annual rate of interest is 11.186 %. (Round to three decimal places.)
Mathematics
1 answer:
Zigmanuir [339]3 years ago
7 0

Answer:

Ans. A) The annual rate that the company charged was 11.996%; B) if they charged you 11.186% annual rate, you would have to pay $41.14

Step-by-step explanation:

Hi, first we have to find out what is the effective 119 days rate and then turn it into an annual rate. This is as follows.

r(Effective119Days)=\frac{44}{1,153} x100=0.038161

So the charged rate was 3.816% effective, 119 days, now let´s make it an annual rate.

r(annual)=(1+0.038161)^{\frac{360}{119} } -1=0.119965

This means that the equivalent rate to 3.816% effective 119 days ys 11.996% effective annually (or just annual).

Now, if they were to charge you 11.186% annual, you would have to make this rate effective 119 days, and then, multiply it by the principal ($1,153). Let´s change the rate first.

r(Effective119Days)=(1+0.11186)^{\frac{119}{360} -1}=0.03568

And the money that you will have to pay in interest is $1,153*0.03568=$41.14

Best of luck

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A person borrowef Rs 16000 from a bank at 12.5% pet annum simple intrest and lent the whole amount to shopkeeper at the sam rate
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Answer:

The amount he gains in 2 years is Rs. 250

Step-by-step explanation:

The parameters of the amount borrowed from the bank are;

The amount borrowed, P = Rs. 16,000

The interest rate of the amount borrowed, R = 12.5%

The number of years, T = 2 years

The simple interest, I = (P × R × T)/100 =  (Rs. 16,000 × 12.5 × 2)/100 = Rs. 4,000

The total amount the person is to pay bank to the bank = P + I = Rs. 16,000 + Rs. 4,000 = Rs. 20,000

The parameters of the amount lent to the shopkeeper are;

The amount lent, P = Rs. 16,000

The compound interest rate of the amount lent, R = 12.5%

The number of years, T = 2 years

The amount he receives from the shopkeeper after 2 years, A = P·(1 + R/n)^(n × T) = Rs. 16,000 × (1 + 0.125/1)^(1 × 2) = Rs. 20,250

The amount he gains in 2 years = The amount he receives from the shop keeper - The amount he gives to the bank = Rs. 20,250 - Rs. 20,000 = Rs. 250

The amount he gains in 2 years = Rs. 250.

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2 years ago
The function h(t) = −5t2 + 20t shown in the graph models the curvature of a satellite dish: graph of parabola starting at zero c
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Answer:

Part 1) Option B: 0 ≤ x ≤ 4

Part 2) Option C: (5x − 1)(2x − 3)

Part 3) Option C: The crop yield decreased by 10 pounds per acre from year 10 to year 20.

Part 4) Option B: f(x) = (2x + 1)(2x − 1)

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Part 6) Option C: (3, 0) and (5, 0)

Step-by-step explanation:

Part 1) we have

h(t)=-5t^{2}+20t

This is a vertical parabola open downward

The vertex is a maximum

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The vertex is the point (2,20) ---> The x-coordinate of the vertex is the midpoint of the x-intercepts

so

The domain is the interval ----> [0,4]

0\leq t\leq 4

The range is the interval ----> [0,20]

0\leq h(t)\leq 20

Part 2) we have

V=10x^{2} -17x+13

where

x is the time in minutes

V is the volume in gallons

we know that

When the trough is empty, the volume is equal to zero

so

For V=0

10x^{2} -17x+3=0

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}

in this problem we have

10x^{2} -17x+3=0

so

a=10\\b=-17\\c=3

substitute in the formula

x=\frac{-(-17)(+/-)\sqrt{-17^{2}-4(10)(3)}} {2(10)}

x=\frac{17(+/-)\sqrt{169}} {20}

x=\frac{17(+/-)13} {20}

x=\frac{17(+)13} {20}=\frac{3}{2}

x=\frac{17(-)13} {20}=\frac{1}{5}

so

10x^{2} -17x+3=10(x-\frac{3}{2})(x-\frac{1}{5})

simplify

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Part 3) we have

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we know that

To find the average rate of change, we divide the change in the output value by the change in the input value

the average rate of change is equal to

\frac{f(b)-f(a)}{b-a}

In this problem we have

f(a)=f(10)=-(10)^{2}+20(10)+100=200  

f(b)=f(20)=-(20)^{2}+20(20)+100=100  

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b=20

Substitute

\frac{100-200}{20-10}

-\frac{100}{10}=-10  ----> is a decreasing function

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Part 4) we have

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<em>Find out the x-intercepts</em>

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4x^{2} -1=0

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x=(+/-)\frac{1}{2}

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t^{2}+14t+85

Remember that

The y-intercept of a function is the value of the function (output value) when the value of x (input value) is equal to zero

In this problem

The expression represent a company's net sales, in billions, from 2008 to 2018

t is the number of years since the end of 2008

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For t=0 -----> represent the end of 2008

(0)^{2}+14(0)+85=85\ billion\ dollars

therefore

The company earned 85 billion dollars in 2008.

Part 6) What are the x-intercepts of the parabola?

we have the points (2,3),(4,-1),(6,3)

This is a vertical parabola open upward

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The equation of a vertical parabola in vertex form is equal to

y=a(x-h)^2+k

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For y=0

(x-4)^2-1=0

Solve for x

(x-4)^2=1

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(x-4)=(+/-)1

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therefore

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