Find the measure of 48.<br> 81<br> 99<br> 48<br> 68 = [?]

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.

7 0

3 years ago

The lengths of a certain species of fish are approximately normally distributed with a given mean ll and standard

RoseWind [281]

How are you? Ok so It probably B but I’m not sure so just wait a few minutes till someone else answers because I’m not sure

5 0

3 years ago

Read 2 more answers

100 POINTS IF U GET THIS RIGHT!

iVinArrow [24]

Answer:

That is the answer

Hope this helps!

3 0

3 years ago

Read 2 more answers

What is the slope of the line given by the equation y= -3x

galben [10]

Answer:

-3

Step-by-step explanation:

The given equation is in slope intercept form.

The form is y=mx+b

This is where "m" is the slope, and "b" is the y intercept.

So in this equation, m=-3.

Therefore, the slope is -3.

3 0

3 years ago

2. The perimeter of a rectangle is 72 cm. The width of the rectangle is 16 cm. What is the area of the rectangle?

tresset_1 [31]

ANSWER
320cm ²

STEP BY STEP
2 widths (16) should equal 32, so you should have 40cm left. Divide 40 by 2 to get one length. Length = 20, width = 16.

So to find the area, you multiply length times width. 20 x 16 = 320

The area is 320cm ²

3 0

3 years ago

Find the measure of 48. 81 99 48 68 = [?]