How to do this maths question?help please.?

Question

the gross product of a certain company in the year 2003 is 11 million dollars.it is projected that the gross product will increase steadily every year by 6%.

a.)find the gross product of the company in 2010

b.)in which year will the gross product of the company just exceed twice the gross product of 2003?

Answer 1

Formula for future worth is:

F = P(1 + i)^n

where:

F = future worth

P = present worth

i = interest

n = number of years

so

1.) F = 11million(1 + 0.06)^7

    F = 16 539 932.85 dollars

2) twice the gross product of 2003 is 22 million so:

   22 000 000 = 11million(1 + 0.06)^n

                n = 11.89 years or 12 years

                2003 + 12 = 2015 ----> the gross amount will double

Answer 2

a)  Use the compound interest formula for future worth (or calculate this out long hand) to solve the first part of the problem.  You need to use the compound interest formula because each years growth is used as the next years starting point (e.g. your growth is left to grow for the next year).

F = P(1+i)ⁿ

Where P=the starting value, r=equals the interest rate (remember that 6%=0.06), n=the number of years or growth, and F=the future value of that growth.

F = P(1+i)ⁿ

F = 11,000,000 (1+0.06)^(2010-2003)

F = 11,000,000 (1.06)^7  Don't forget to work the exponent first.

F = 11,000,000 (1.50)  I approximated the value in the ()

F = 16,539,932.84

b)

To solve this you need to use "The rule of 72" which says that if you divide 72 by the interest rate (actual percentage) it will tell you how many years it will take to double an investment.

72/6=12  It will take about 12 years to double your money.

2003+12=2015  Your investment will have doubled by the year 2015.

To check your calculations, plug the 12 back into your original

formula for future value.

F = P(1+i)ⁿ

F = 11,000,000 (1+0.06)^12

F = 11,000,000 (1.06)^12

F = 11,000,000 (2.012)

F = 22,134,161.19

Answer 3

Gross Product in 2003 = $11,000,000

Increases by 6% ==> 11,000,000 • 6% = $660,000

Question #1: Gross Company Product

Target Year - Starting year = total years.

2010 - 2003 = 7

$660,000 • 7 = $4,620,000

So, in four years the company will have made $4,620,000 which means that the gross of the company is:

$11,000,000 + $4,620,000

$15,620,000 (<==ANSWER!!)

Question #2: Which year will the company double the Gross Product?

$11,000,000 • 2 = $22,000,000

Let "x" represent the number of years to reach the double Gross Product.

11,000,000 + 660,000x = 22,000,000

660,000x = 22,000,000 - 11,000,000

660,000x = 11,000,000

x = 11,000,000 ÷ 660,000

x = 16 and 2/3

So, it would take 16 years and 2/3 of a year or 16 years and 8 months to double the company's Gross Product. So,

2003 + 16

2019 (<==ANSWER!!)

It will be in the year 2019 that the company will double the Gross Product.

Hope I helped!

Answer 4

your gross product rises by 6% every year.

in the second year you will have 11 mil * 6% additionally to your 11 mil, which adds up to 106% of 11 mil.

the following year you have 106% of the 106% you got in year 2.

you can write it this way: 11 mil $ * 106% * 106%

or shorter: 11 mil $ * 1,06 ²

for any amount n of passed years you know the gross product by substituting that exponent with your number of years:

GP(n) = 11 mil. $ * 1.06 ^ n

a) 2010 is seven years later - n = 7

GP = 11 mil $ * 1.06 ^ 7 = 16539932,84 mil $

b) you want to know for which n

11 mil $ * 2 = 11 mil. $ * 1.06 ^ n

11 mil $ * 2 = 11 mil $ * 1.06 ^ n | / 11 mil

2 = 1.06 ^ n | log

n = log 1.06 ( 2)

n = 11.89

after 11.89 years you will have 11 mil $ * 2 = 22 mil. $

Answer 5

a.)int=$4.62M  Gross would be$15,620,000

.

Answer 6

Answer:a) 17,53232882 million dollars

b)2014

2003 11 0,66 11,66

2004 11,66 0,6996 12,3596

2005 12,3596 0,741576 13,101176

2006 13,101176 0,78607056 13,88724656

2007 13,88724656 0,833234794 14,720481...

2008 14,72048135 0,883228881 15,603710...

2009 15,60371023 0,936222614 16,539932...

2010 16,53993285 0,992395971 17,532328...

2011 17,53232882 1,051939729 18,584268...

2012 18,58426855 1,115056113 19,699324...

2013 19,69932466 1,18195948 20,8812841...

2014 20,88128414 1,252877049 22,134161...