C2 Question (geometric series)

Hi,
I've got a question on geometric series (at least i think it is on GP). here is the question...

Amy plans to join a savings scheme in which she will pay in £500 at the start of each year.

One scheme that she is considering pays 6% interest on the amount in the account at the end of each year.
For this scheme,
(a) find the amount of interest paid into the account at the end of the second year, (I done this)
(b) show that after interest is paid at the end of the eighth year, the amount in the account will be £5246 to the nearest pound. (Stuck here!!! :frown:

)

Another scheme that she is considering pays 0.5% interest on the amount in the account at the end of each month.
(c) Find, to the nearest pound, how much more or less will be in the account at the end of the eighth year under this scheme.

tnx in advance!

Reply 1

generalebriety

Hmm, started to answer, then misread and got £797 :smile:

Ok... at the end of the first year she will have 500*1.06.

Then she pays another 500 in so she has 500*1.06 + 500 = 500*(1.06 + 1). At the end of the second year she has 500*(1.06 + 1)*1.06 = 500*(1.06^2 + 1.06).

Then she pays in an extra 500, so she has 500*(1.06^2 + 1.06) + 500 = 500*(1.06^2 + 1.06 + 1). Then at the end of the third year she has 500*(1.06^3 + 1.06^2 + 1.06)...

What a disgusting question. Anyway, it seems to me that you'll have to work out (1.06^8 + 1.06^7 + ... + 1.06^2 + 1.06) and multiply the whole lot by 500.

Then part (c), do the same, just with 1.005^12 (think about it), and some lovely subtracty stuff.

Edit: answers I got were (b) £5246 and (c) £40.