Each year, Andy pays into a savings scheme - Edexcel - A-Level Maths Pure - Question 5 - 2018 - Paper 1

Let $d = 80$ for Kim.

For Kim’s payments:

• In the first year, she pays £130.
• Yearly increase is £80.

To find the total amount Kim has paid by year N, the sum formula for the first N terms is applied:

$S_{Kim} = \frac{N}{2} \times [2 \times 130 + (N-1) \times 80]$

Now, for Andy:

• Total payments for Andy by year N:

$S_{Andy} = \frac{N}{2} \times [2 \times 600 + (N-1) \times 120]$

Setting up the equation based on the provided information:

At year N, Andy has paid twice as much as Kim:

$S_{Andy} = 2 \times S_{Kim}$

This leads to:

$\frac{N}{2} \times [2 \times 600 + (N-1) \times 120] = 2 \times \frac{N}{2} \times [2 \times 130 + (N-1) \times 80]$

This simplifies down to:

$20N = 360N$

Solving for $N$ gives:

$N = 18$

Therefore, the value of N is 18.