Math Is Fun Forum

Andrew1930

Member

Registered: 2015-03-23

Posts: 5

Annuity, regular investment calculation - formula needed!

Hello All.

What a great site : I have an exam to sit in the UK late April and the sections on Compound Interest and Annuities have been invaluable.

I have thanked Rod privately but I will do so publicly here : Thank You Rod!

OK - here is my question - it is one of the "mock exam questions" that I am working through before the exam.

"Andrew invested $500 at the end of every year for 5 years at an interest rate of 6%.
What is his accumulated value at the end of the period?"

The correct answer is $2,818.35

But I cannot find a formula to calculate the answer.

I have looked on the Maths Is Fun site and elsewhere.

I'd be really grateful for any help.

Best regards and thanks again,

Andrew.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Annuity, regular investment calculation - formula needed!

hi Andrew1930

Welcome to the forum. 

Yes, it's a great site!

I don't get quite that value (few cents out) which may just be due to rounding after each year (I didn't but maybe the questioner did).

It doesn't say there is any initial investment, so let's say there isn't.

At the end of year 1 the investment is 500.

At the end of year 2 that has grown by a factor of 1.06 then another 500 = 500x1.06 + 500

At the end of year 3 that has grown by a factor of 1.06 then another 500 =

Then x by 1.06 again and add another 500 =

And one more time to get to the end of year 5

The bracket is a geometric progression with first term a = 1 and common ratio r = 1.06

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Andrew1930

Member

Registered: 2015-03-23

Posts: 5

Re: Annuity, regular investment calculation - formula needed!

Bob,

That is fantastic!

I understood your reply on the very first reading and I have been able to replicate the formula easily on my calculator (needed for the exam!).

I have couple of more queries and will post these in the next couple of days.

I am very grateful to you - many thanks and best regards,

Andrew.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,895

Re: Annuity, regular investment calculation - formula needed!

Hi Andrew1930,

Yes, great answer from Bob with those workings! Even I understood them!

I found this formula on the net:

Where:
P = principal after n years
M = deposit amount per period
i  = annual interest rate
q = number of equal time periods per year
n = number of years

Because q=1, the formula simplifies to Bob's.

This formula may be of interest for tackling other problems: eg,
M = $250 deposit at the end of every six months
i  = 6% annual, but interest calculated six-monthly
q = 2
n = 5

Answer: P = $2865.97

Last edited by phrontister (2017-02-22 00:24:47)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Andrew1930

Member

Registered: 2015-03-23

Posts: 5

Re: Annuity, regular investment calculation - formula needed!

Many thanks phrontister.
Best regards,
Andrew.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,895

Re: Annuity, regular investment calculation - formula needed!

Hi Andrew,

It may be worthwhile to learn the general formula I gave as it could help deal with a tricky exam question.

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson