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# Arithmetic Progression Difficulty

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1. So...

Someone invests £1000 in an account offering an interest rate of 5% each year. How many years will it take to get £1500.

I used the equation Sn=n/2[2a+(n-1)d] and I have made d=1.05, a=1000 and Sn=1500. I got a quadratic equation which came out at about 1.5 and -2000 which can't be right.

So have I made a glaring error or used the wrong equation?Any help/advice would be great.Thanks
2. (Original post by Pokeyguy20)
So...

Someone invests £1000 in an account offering an interest rate of 5% each year. How many years will it take to get £1500.

I used the equation Sn=n/2[2a+(n-1)d] and I have made d=1.05, a=1000 and Sn=1500. I got a quadratic equation which came out at about 1.5 and -2000 which can't be right.

So have I made a glaring error or used the wrong equation?Any help/advice would be great.Thanks
It's more of a geometric series. After the first interest payment, you have 1000*1.05. The second, you have 1000*1.05^2...

Edit: I may have made a mistake, but you've figured it out.

Well done
3. Sorry to waste your time it is actually a 'simple interest rate' which means it's only 5% each year of £1000. So the answer comes out as 11 years when plugged into the ap formula.

That's why you're supposed to RTFQ!!

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