Thread: 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

Hello Stonehambey

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

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

At the end of year $\displaystyle n$, the total amount is £$\displaystyle 1000(1 + 1.05 + \dots )$. 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 $\displaystyle n$ terms?

Can you complete it now?

Grandad