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.
Answers
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 ×
Or, Value of business after 2 years = initial value of business ×
Or, Value of business after 2 years = 30,000 ×
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 ×
Or, Value of business after 5 years = initial value of business ×
Or, 95,000 = 80,000 ×
Or, =
Or, = 1.18
Or, 1 + =
Or, 1 + = 1.033
Or, = 1.033 - 1
or, = 0.033
∴ r = 0.033 × 100
i.e r = 3.3 %
Hence, The rate of increase in value is 3.3% Answer