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A level maths,please help

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,

b) show that after interest is paid at the end of the 8th year, the amount in the account will be £5246 to the nearest pound.

Another scheme that she is considering pays 0.5% interest on the amount 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 8th year under this scheme.

I am not understanding part b.Like,every year Amy is depositing 500 pounds,so how am I supposed to calculate the total amount? NOW,I did use sum of GP formula to calculate the total amount ,that 500(1.06)(1.06^8-1)/1.06-1 but I am not understanding why exactly it is giving the correct answer,even though Amy is depositing Extra 500 pounds EVERY year.
Can anyone please explain it to me?(Edexcel C2 Solomon Paper E)
(edited 6 months ago)
I think I’ve worked it out.

At the start of the first year, there are £500, but at the end of the year, 6% interest is paid and so there should be £[500(1.06)] in the account.

At the start of the next year, another £500 is paid and so there should be £[500(1.06) + 500]. Again, another 6% interest is paid at the end of the year and multiplying the whole expression by 1.06 gives £[500(1.06)^2 + 500(1.06)] in the account at the end of the year.

Now if you can spot a pattern, you may realise that if you add 500 onto the previous amount in the bank, then multiply by 1.06 and repeat, you form a geometric series. See if you can work out what the values of a and r are for this geometric series.
(edited 6 months ago)
Reply 2
Original post by TypicalNerd
I think I’ve worked it out.

At the start of the first year, there are £500, but at the end of the year, 6% interest is paid and so there should be £[500(1.06)] in the account.

At the start of the next year, another £500 is paid and so there should be £[500(1.06) + 500]. Again, another 6% interest is paid at the end of the year and multiplying the whole expression by 1.06 gives £[500(1.06)^2 + 500(1.06)] in the account at the end of the year.

Now if you can spot a pattern, you may realise that if you add 500 onto the previous amount in the bank, then multiply by 1.06 and repeat, you form a geometric series. See if you can work out what the values of a and r are for this geometric series.

OH MY GOODNESS!!!!
THANK YOU SO MUCH DUDE!!!!!!!
FINALLY I CAN SEE THE SEQUENCE 😭😭😭😭😭
I had invested around 5 hours in this single problem for the last 2 days,and my P2 exams are on Tuesday.
THANK YOU SOOO MUCH!!!!!!

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