Geometric series Q

dtfo

This is from the 2012 sec sample , question 8 c , I have an answer but Im not 100% sure Im right, has anyone done it?

Pádraig is 25 years old and is planning for his pension. He intends to retire in forty years’ time,
when he is 65. First, he calculates how much he wants to have in his pension fund when he retires.
Then, he calculates how much he needs to invest in order to achieve this. He assumes that, in the
long run, money can be invested at an inflation-adjusted annual rate of 3%. Your answers
throughout this question should therefore be based on a 3% annual growth rate.

(c) Pádraig wants to have a fund that could, from the date of his retirement, give him a payment
of €20,000 at the start of each year for 25 years. Show how to use the sum of a geometric
series to calculate the value on the date of retirement of the fund required

MathsManiac

You write down the "present values" on the date of retirement of all the future payments, and then note that this is a finite geometric series, and work out its sum.

20000 + 20000/1.03 +20000/(1.03)^2 + ... + 20000/(1.03^24).

It's a geometric series with a = 20000, r = 1/1.03, and n=25.

dtfo

Thanks, thats what I had