3. Error Analysis A classmate began an indirect

What is the rule of 72 used to determine? A. the approximate time it takes an investment to triple in value B. the approximate t

ValentinkaMS [17]

Answer:

Step-by-step explanation:

This can be derived using the formula to calculate future value of an amount which is given as:

FV=PV(1+i)^{n}

Where

FV is the future value

PV is the present value

i is the compound interest rate

n is the time period

To calculate how much time it takes to triple an amount, let's substitute $1 in place of PV and $3 in place of FV in the above equation.

3=(1+i)^{n}

Taking natural log on both sides, we get

log_{e} 3= n log_{e}(1+i)

n={\log_{e}3}/{log_{e}(1+i)}....................(1)

Using some log magic, this formula can also be written as

n=log_{(1+i)}3................(2)

Both equations (1) and (2) work fine.

(b)

In order to derive a rule 72 style formula start from equation (1) above. In that formula, we can say that for small values of interest rate,

log_{e}(1+i) ~ i ( This is a property of log)

Substituting this is equation (1), we get

n=log_{e}3/{i}

n={1.098}/{i}

Since, we want to use i as an integer and not as a percentage (so, 3% will be used as 3 and not 0.03), we multiply the RHS by 100

n={109.8}/{i}

and then to make it cleaner, we round off 109.8 to 110.

n={110}/{i}

Now, many times, people round this 109.8 off to 114. This is to make the calculations a little bit easier as 114 is number that has a lot of factors. So, if the numerator is rounded off to 114, the formula becomes

n={114}/{i}

6 0

3 years ago

Read 2 more answers

Amar and his friends went to a movie at 3:55 P.M. The movie ended at 5:30 P.M.

kotegsom [21]

Answer: the movie was 1 hour and 35 minutes and Amar got home at 6:15 P.M.

Step-by-step explanation:

to find out how long the movie was you have to find the distance between the time frames 3:55 and 5:30.

3:55+1 hour= 4:55

4:55+5 minutes= 5:00

5:00+30 minutes= 5:30

Add the times to find how long the movie was.

This is how I found how long the movie was.

To find out when Amar got home you have to do the same thing as well.

5:30+30 minutes= 6:00

6:00+15 minutes= 6:15

Hope this helps!

6 0

3 years ago

Your teacher has told you that she will drop your "worst" test.

Sever21 [200]

Test one would be the worst one

6 0

3 years ago

Read 2 more answers

A company currently has an advertisement that covers a bill board that is 30 ft wide by 70 ft high. The company wants to reduce

Sedbober [7]

Given :

A company currently has an advertisement that covers a bill board that is 30 ft wide by 70 ft high. The company wants to reduce the same advertisement to fit on a new billboard that is 25 ft wide by 40 ft high.

To Find :

The dimensions of the largest advertisement that will fix on the billboard without cropping the advertisement.

Solution :

Area of original bill board :

$A_i=30\times 70 = 2100\ ft^2$

Area of new bill board :

$A_f=25\times 40 = 1000\ ft^2$

Since, new bill board can be completely fitted in original bill board as its length and breadth both are smaller than that.

So, the dimensions of the largest advertisement that will fix on the billboard without cropping the advertisement is equal to 1000 ft².

Hence, this is the required solution.

7 0

4 years ago

Classify each pair of labeled angles as complementary, supplementary, or neither.

professor190 [17]

Supplementary, complementary, neither

6 0

3 years ago