Question

Mrs Bean bought a business at the start of 2006
The business was then valued at £30,000
Since Mrs Beans takeover, the business has consistently achieved a 2% yearly increase in value.
a) work out the value of the business at the end of 2018.
Give your answer correct to the nearest £100

Another business was valued at £80,000 at the start of 2013.
In 5 years the value of his business raised to 95,000
This is equivalent to a yearly increase of x%.
b) find the value of x
Give your answer correct to 2 significant figures.

Answer 1

$A = P(1+\frac{r}{n} )^{nt} \\P = 30000\\r = .02\\n = 1 time a year\\t = 2018 - 2006\\\\A = 30000(1 + .02/1)^{1*12} \\A = \ 38047.25\\----------------\\Solve for 'r'\\95000 = 8000(1 + r/1)^{1*5} \\95000 = 8000(1+r)^{5} \\11.875 = (1 + r)^{5}\\1.64031 = 1+r$

I see I did something wrong in the 2nd part, just take the first question as the right one.

Answer 2

The required value of the business at the end of 2018 is $38,000.

Given that,

Mrs. Bean bought a business at the start of 2006

The business was then valued at £30,000

Since Mrs. Beans takeover, the business has consistently achieved a 2% yearly increase in value.

Another business was valued at £80,000 at the start of 2013.

In 5 years the value of his business raised to 95,000

This is equivalent to a yearly increase of x%.

We have to find,

The value of the business at the end of 2018.

According to the question,

• The value of the business at the end of 2018.

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

Where, P=30,000, r = 2%=0.02, t = 2018-2006 = 2012,  n=1year

Therefore,

$A = 30,000 (1+\frac{0.02}{1} )^{1\times2012}\\A = 30,000(1.2)^{2012}\\A = 38047.25$

It is nearest to A = $38,000.

Hence, The required value of the business at the end of 2018 is $38,000.

For more information about Percentage click the link given below.

https://brainly.com/question/12431044