Math Is Fun Forum

CJVR

Member

Registered: 2013-08-22

Posts: 1

Compound interest on investment

I am new to the forum, so hello to everybody.  Please help, I would like to know the formula for the following situation:  The investor takes out an investment of $450 per month every month for 5 years, interest rate is 10% per annum, how do I calculate the total value after 5 years? This can be calculated easily on a financial calculator, but I would like to know the formula. Thank you.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Compound interest on investment

hi CJVR

Welcome to the forum.

I don't know it either but I'll have a go at working it out.

Firstly I want to work out a monthly interest multiplier that is equivalent to 10% per annum

The per annum multiplier would be x 1.1 so to get a per month multiplier:

Now work through a few months to establish a pattern.

Start of month one

End of month one

Start of month two

End of month two

Start of month three

End of month three

So after 60 months

Using the formula for the sum of a GP

In the screen shot below I have worked through 3 months like this and then used the formula to check the formula gives the same value.

http://www.mathsisfun.com/algebra/seque … etric.html

As I've just made this up it would be great to know that a financial calculator gives the same results.

NEXT DAY EDIT:

I tried http://www.thisismoney.co.uk/money/savi … lator.html

It made it £34846.68 whereas my formula made it £34727.28 (using Excel)

This calculator only accepts interest rates to 2 dp so it is not clear whether my formula is wrong or whether their's is insufficiently accurate.

I'll try to find a more accurate one.

A LITTLE LATER:

http://www.calculatorweb.com/calculator … calc.shtml

gives 35877.46

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Compound interest on investment

Final offering for now:

I worked it month by month in Excel and working to 10 dp. 

The screen shot below shows the last few months.  I deliberately 'overshot' in case one should be counting 59 or 61 months.

Small rounding errors will build up over 60 iterations so I claim my answer is the most accurate. 

Bob

---

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