Year 12s: what will be the first way you research your future options? >>

C1 Sequences

Each year, for 40 years, Anne will pay money into a savings scheme. In the first year she pays £500. Her payments then increase by £50 each year, so that she pays £550 in the second year, £600 in the third year, and so on.

(a) Find the amount that Anne will pay in the 40th year.

(b) Find the total amount that Anne will pay in over the 40 years.

Over the same 40 years, Brian will also pay money into the savings scheme. In the first year he pays in £890 and his payments then increase by £d each year.

Given that Brian and Anne will pay in exactly the same amount over the 40 years,

(c) find the value of d.

Reply 1

Jonny W

(a)
The payment goes up 39 times, by 50 pounds each time.

500 + 39*50 = 2450

(b)
40*(average payment)
= 40*(1/2)(first payment + last payment)
= 40*(1/2)(500 + 2450)
= 59000

(c)
Brian pays in 40*(1/2)(890 + 890 + 39d).

Solve 40*(1/2)(890 + 890 + 39d) = 59000.