Final answer:
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:

Substituting the values we get:

£95000/£80000 = 1.1875

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%.