# Thread: AP/GP problem

1. ## AP/GP problem

Hi

I'm having problems with part c of the question below

http://stonehambey.com/Images/C2Q.png

Because they're adding 1k every year and then the percentage interest is added (almost like a cross between an AP and a GP), it's left me feeling confused as how to solve it. I'm pretty sure I'm missing something obvious though

Any pointers would be much appreciated

Regards,

Stonehambey

2. ## Ap/gp

Hello Stonehambey

At the end of year 1, when the second payment of £ $1000$ has been made, the first investment of £ $1000$ will be worth £ $1000 \times 1.05$. So the total amount in the savings account is now £ $1000 + £1000 \times 1.05 = 1000(1 + 1.05)$.

At the end of year 2, when the third payment has just been made, the first investment is now worth £ $1000 \times 1.05^2$ and the second payment is worth £ $1000 \times 1.05$. So the total amount is now £ $(1000 + 1000 \times 1.05 + 1000 \times 1.05^2) = 1000(1 + 1.05 + 1.05^2)$.

At the end of year $n$, the total amount is £ $1000(1 + 1.05 + \dots )$. Can you see what it will be?

The series in the brackets is a GP, where the first term is ? and the common ratio is ? So what is the sum to $n$ terms?

Can you complete it now?