Question

A business was valued at £80000 at the start of 2013. In 5 years the value of this business raised to £95000. this is equivalent to a yearly increase of x%.

Find out the value of x.
give your answer correct to 2 significant figures.

Answer 1

The yearly percentage increase, x%, of the business value over 5 years is calculated using the compound interest formula. After substituting the given values into the formula and solving, the yearly increase x is found to be approximately 3.5% when rounded to two significant figures.

Step-by-step explanation:

To calculate the yearly percentage increase, x%, of the business value over the 5 year period, we will use the formula for compound interest which is A = P(1 + r)^n, where:

• A is the final amount of money after the interest
• P is the principal amount (the initial amount before the interest)
• r is the yearly interest rate (as a decimal)
• n is the number of years

In this case, A = £95000, P = £80000, and n = 5 years.

We have to solve for the interest rate, r, so we rearrange the formula to get:

`r = (A/P)^((1/n)) - 1`

Substituting the values we get:

`r = ( \£95000/ \£80000)^((1/5)) - 1`

£95000/£80000 = 1.1875

`(1.1875)^((1/5)) = 1.03523 \ approximately`

So r would be 1.03523 - 1 = 0.03523, or 3.523%

Therefore, the yearly increase x to the nearest two significant figures is 3.5%.

Answer 2

20%

Step-by-step explanation:

Value increased in 5 years = £95000 - £80000 = £5000

Value increase in 1 year =5000/5 = 1000

Increase % = (1000/5000 ) * 100 = (1/5) *100 = 20%