Question

Mrs Bean bought a business at the start of 2006 The business was then valued at £ 30 000 Since Mrs Bean's takeover, the business has consistently achieved a 2% yearly increase in value. a) Work out the value of the business at the start 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 this 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

Answer:

(a) The Value of business in 2008 is 31212 pound .

(b) The rate of increase in value is 3.3%

Step-by-step explanation:

Given as ;

At The start of 2006, the value of business = 30,000 pound

The rate of increase = r = 2 %

Let The value of business in 2008 = x pound

Time period = t = 2 years

According to question

Value of business after n years = initial value of business × $(1+\dfrac{rate}{100})^{time}$

Or, Value of business after 2 years = initial value of business × $(1+\dfrac{2}{100})^{2}$

Or,  Value of business after 2 years = 30,000 × $(1+\dfrac{2}{100})^{2}$

Or,   Value of business after 2 years = 30,000 × (1.02)²

or,  Value of business after 2 years = 30,000 × 1.0404

Or, Value of business after 2 years =  31212 pound

Hence, The Value of business in 2008 is 31212 pound . Answer

(b) At The start of 2013, the value of business = 80,000 pound

The rate of increase = r %

The value of business in 2013 = 95,000 pound

Time period = t = 5 years

According to question

Value of business after n years = initial value of business × $(1+\dfrac{rate}{100})^{time}$

Or, Value of business after 5 years = initial value of business × $(1+\dfrac{r}{100})^{5}$

Or,  95,000 = 80,000 × $(1+\dfrac{r}{100})^{5}$

Or,  $(1+\dfrac{r}{100})^{5}$ = $\dfrac{95,000}{80,000}$

Or, $(1+\dfrac{r}{100})^{5}$ = 1.18

Or, 1 + $\dfrac{r}{100}$ = $(1.18)^{\dfrac{1}{5}}$

Or, 1 + $\dfrac{r}{100}$ = 1.033

Or,  $\dfrac{r}{100}$ = 1.033 - 1

or,  $\dfrac{r}{100}$ = 0.033

∴   r = 0.033 × 100

i.e  r = 3.3 %

Hence, The rate of increase in value is 3.3%  Answer