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3 years ago

Help !!!!!!!!!!!!!!!!!!!!!

Mathematics

1 answer:

igor_vitrenko [27]3 years ago

6 0

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If Tanisha has $1000 to invest at 7% per annum compounded semiannually, how long will it be before she has $1600? If the co

Sphinxa [80]

Answer:

Using continuous interest 6.83 years before she has $1600.

Using continuous compounding, 6.71 years.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

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

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.

Continuous compounding:

The amount of money earned after t years in continuous interest is given by:

$P(t) = P(0)e^{rt}$

In which P(0) is the initial investment and r is the interest rate, as a decimal.

If Tanisha has $1000 to invest at 7% per annum compounded semiannually, how long will it be before she has $1600?

We have to find t for which $A(t) = 1600$ when $P = 1000, r = 0.07, n = 2$

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

$1600 = 1000(1 + \frac{0.07}{2})^{2t}$

$(1.035)^{2t} = \frac{1600}{1000}$

$(1.035)^{2t} = 1.6$

$\log{1.035)^{2t}} = \log{1.6}$

$2t\log{1.035} = \log{1.6}$

$t = \frac{\log{1.6}}{2\log{1.035}}$

$t = 6.83$

Using continuous interest 6.83 years before she has $1600

If the compounding is continuous, how long will it be?

We have that $P(0) = 1000, r = 0.07$

Then

$P(t) = P(0)e^{rt}$

$1600 = 1000e^{0.07t}$

$e^{0.07t} = 1.6$

$\ln{e^{0.07t}} = \ln{1.6}$

$0.07t = \ln{1.6}$

$t = \frac{\ln{1.6}}{0.07}$

$t = 6.71$

Using continuous compounding, 6.71 years.

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3 years ago

Find the volume of the sphere. <br> Either enter an exact answer in terms π or use 3.14 for π

Lunna [17]

The equation for volume of a sphere is (4/3)(pi)(r)^3. So you would plug in he radius 9 into the equation. It would simplify to equal (4/3)(pi)(729). It simplifies further to equal (972)(pi)

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4 years ago

25 POINTS FOR WHO EVER CAN HELP ME!!!

RideAnS [48]

Try A, $5000. I did 550 divided by 11, which is 50, then multiplied by 10 to find 10%, then multiplied the 10%, which was 500, by 10 to get 100% which is 5,000

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3 years ago

Dream borrowed $500 at an interest rate of 8%. At the end of the loan period, she had to pay back $530. How long was the loan fo

Aliun [14]

Answer:

The loan was for 9 months only

Step-by-step explanation:

In this question, we are concerned with calculating the time taken for a loan om an interest to be paid back

To calculate this, we use the simple interest formula

Mathematically;

I = PRT/100

where P is the principal which is the amount borrowed and that is $500 according to the question

R is the rate which is 8% according to the question

Interest can be calculated by subtracting the principal from the amount paid back = 530-500 = 30$

We now plug these values into the equation

30 = (500 × 8× T)/100

100 × 30 = 4000T

T = 3000/4000

T = 0.75 (same as 0.75 × 12 months = 9 months)

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3 years ago

If p(x) = 2x2 – 4x and q(x) = x – 3, what is (p circle q) (x)?

mamaluj [8]

Answer:

2x^2 - 16x + 30

Step-by-step explanation:

Here, we want to get the composite function;

p•q(x)

All we have to do here is to replace the x value in p(x) by the totality of q(x)

we have this as ;

= 2(x-3)^2 - 4(x-3)

= 2(x^2 -6x + 9) - 4(x-3)

= 2x^2 -12x + 18 -4x + 12

= 2x^2 - 16x + 30

8 0

3 years ago

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