Math Is Fun Forum

markosheehan

Member

Registered: 2016-06-15

Posts: 51

financial maths and geometric series

john is 25 years old and is planing for his pension . he intends to retire in 40 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 to achieve this. he assumes that in the long run money can be invested at an inflation adjusted annual rate of 3%. your answers should be based on a 3% annual growth rate

(I) john wants to have a fund from the date of his retirement, give him a payment of £20000 at the start of each year for 25 years.show how to use the sum of geometric series to calculate the value on the date of retirement the fund required.

i cant work this out. the answer is 358710.84 by the way

Bob

Administrator

Registered: 2010-06-20

Posts: 10,166

Re: financial maths and geometric series

hi markosheehan,

Here's the sort of calculation that should do the job:

Each year interest is gained at 3% so a multiplier for the change in principal is m = (1+3/100) = 1.03

REVISED ANSWER:

He is taking out 20000 from his pot each year of retirement for 25 years then start with a pot = Q.

At the end of retirement year 1 he has (Q-20000)m

At the end of retirement year 2 he has (Qm - 20000m - 20000)m

and so on.  After 25 years this will be equal zero from which you can work out Q.

Qm^24 - 20000m^25 - .... -1 = 0

So

Hope that helps.

Bob

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Children are not defined by school ...........The Fonz
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thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: financial maths and geometric series

Last edited by thickhead (2016-08-21 04:32:39)

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
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markosheehan

Member

Registered: 2016-06-15

Posts: 51

Re: financial maths and geometric series

thanks for your help but i dont even understand the question. why does the amount he needs each year go down for example the first year he needs 20000 and then the next year he only needs 20000/1.03 and so on why is the amount of money he needs going down

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: financial maths and geometric series

If you need 20000 after 1 year you need to invest 20000/1.03 today so that with interest it will become 20000.
If you need 20000 after 2 years you need to invest 20000/1.03^2 today for it will accumulate interest for 2 years.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

markosheehan

Member

Registered: 2016-06-15

Posts: 51

Re: financial maths and geometric series

ok thanks i get it now