A company predicts a yearly profit of £120 000 in the year 2013 - Edexcel - A-Level Maths Pure - Question 5 - 2013 - Paper 6

To calculate the total predicted profit from 2013 to 2023, we need to find the sum of the geometric series:

S_n = a rac{1 - r^n}{1 - r}

Where:

• $a = £120,000$,
• $r = 1.05$,
• $n = 11$ (for the years from 2013 to 2023).

Using the formula:

S_{11} = 120000 rac{1 - (1.05)^{11}}{1 - 1.05}

Calculating $(1.05)^{11}$:

$(1.05)^{11} ext{ is approximately } 1.7137$

Now substituting back into the formula:

S_{11} = 120000 rac{1 - 1.7137}{-0.05} = 120000 rac{-0.7137}{-0.05} $= 120000 imes 14.274$ $= 1712880$

Thus, the total predicted profit for the years 2013 to 2023 is approximately £1,712,880.