1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
dmitriy555 [2]
3 years ago
8

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

mpounding is​ continuous, how long will it​ be?
Mathematics
1 answer:
Sphinxa [80]3 years ago
7 0

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.

You might be interested in
5v2-8=442 what is the square root
Drupady [299]

Answer: 3√10 or v=−3√10

Step-by-step explanation:

5 0
3 years ago
Tell whatever the fraction 4 / 10 is in the simplest form (yesor no)
Umnica [9.8K]
No, it's simplest form would be 2/5.
8 0
3 years ago
Read 2 more answers
Please help asap I genuinely cannot figure this out
Gemiola [76]

Answer:

C

Step-by-step explanation:

We can use the factored form of the quadratic equation, given by:

y=a(x-p)(x-q)

Where <em>a</em> is the leading coefficient and <em>p</em> and <em>q</em> are the zeros.

We have zeros <em>x</em> = -2 and <em>x</em> = 3. So, let <em>p</em> = -2 and <em>q</em> = 3:

y=a(x+2)(x-3)

Next, we are given that our <em>y-</em>intercept is (0, -30).

In other words, when <em>x</em> = 0, <em>y</em> = -30. So:

-30=a(0+2)(0-3)

Solve for <em>a:</em>

<em />-30=-6a\Rightarrow a=5<em />

<em />

Hence, our factored equation is:

\displaystyle y=5(x+2)(x-3)

For the standard form, expand:

y=5(x^2-3x+2x-6)

Simplify:

y=5(x^2-x-6)

Distribute:

y=5x^2-5x-30

Our answer is C.

4 0
3 years ago
Read 2 more answers
URGENT!! Please answer this! (In your own words) The best answer gets BRAINLIEST!
Fantom [35]

Answer:

The area is 97.5.

Step-by-step explanation:

The formula for finding the area of a rectangle is Length x Width.

At the bottom it says 5 ft and 10 ft. 10 + 5 = 15, therefore the length is 15.

On the right it says 12 ft, therefore the width is 12 ft.

Since the formula is Length x Width, I did 15 x 12, I attached a file below showing the multiplication process.

15 x 12 = 180.

Therefore, the area of the rectangle is 180.

But, from what it appears from the picture, it's only the shaded area needed.

So, the unshaded areas needed to be subtracted from the rectangle.  

Starting with the triangle on the right, the area for a triangle is the base times the height divided by 2, 10 is the base and 12 is the height. 10 x 12 / 2 = 60, multiplication shown below.

The two sides are the same length, making the height for the other side 12 as well.

According to the rectangle, 3 feet does not belong there.

12 - 3 = 9 ft.

Now, the base is 5 ft and the height is 9 ft.

The formula is base x height divided by 2.

5 x 9 / 2 = 22.5, multiplication shown below.

Now, I had known that the 2 shaded areas were 22.5 and 60.

So, I did 180 - 60 - 22.5 = 97.5

Therefore, the area for the shaded part of the rectangle is 97.5.

I sincerely hope this helped! Have a great day, and good luck! :) :)

7 0
2 years ago
EN LA FRUTERIA "LA CANASTA" SE ANUNCIA EL KG DE NARANJAS A $13.50, ¿Cuánto PAGARA DON JOSE POR COMPRAR 2.6KG? Y SI A DOÑA PAULA
ladessa [460]

Answer:

hola soy dora

Step-by-step explanation:

soy stan kim namjoon

7 0
2 years ago
Other questions:
  • A file that is 278 megabytes is being downloaded. If the download is 14.3% complete, how many megabytes have been downloaded? Ro
    14·1 answer
  • In a discus competition, an athlete threw the discus 63.37 meters, and 63.7 meters.Order the distances from least to greatest
    14·1 answer
  • Ray, a Montana resident, is on a fishing trip in Canada. He plans to buy 50 yards of fishing line at a bait and tackle store. Th
    14·1 answer
  • Quadrilateral RSTU is a rectangle with diagonal RT. If rtu 8x + 4 and str = 3x – 2, find x
    12·1 answer
  • How do u do this? HELPPPPPPPPPPPP
    5·1 answer
  • What are the y and x intercepts for -5x-4y=10
    5·2 answers
  • Write the equation of the line shown (3,6) (3,-4)
    5·1 answer
  • What is Y equals -2/3 X +4 in standard form?
    5·1 answer
  • The population of Philadelphia in 1990 was 1,585,577. In 2010 the population was 1,526,006. What is the percent change the popul
    13·1 answer
  • Simplify the expression (7x² - 3x) + (11x² - x - 7) A. 18x² + 2x + 7 B. 4x² - 4x - 7 C. 18x² - 2x - 7 D. 18x² - 4x - 7
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!