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# Help with compound interest problem!!

Hoping someone can help - it was my daughter's homework but she couldn't do it and now its just nagging at me. It is compound interest which I could work out on a yearly basis but what if this investment went on for 50 or 60 years. There must be a formula that I can use?
So, if you invest £100 at 5% interest and at the end of each year you add another £100 ie at the end of year 1 you would have £205.
Ant mathematical stars out there?
Thanks

Original Poster

melipona;4536831

http://gs.fanshawec.ca/tlc/math270/3_3_compound_Interest.htmhttp://www.moneychimp.com/calculator/compound_interest_calculator.htm

Thanks for this (Rep added) - but what I'd really like to know is what is the formula that the calculator uses? It does exactly what I want, ie adds to the capital sum each year but doesn't show me how it is calculating.
Strange how these puzzles can get hold of you isn't it?

Thanks again:thumbsup:

The calculator could just be doing the iterations
0
*1.05 +100 = 100
*1.05 +100 = 205
*1.05 +100 = 315
etc.
If there's any mathemeticians around, they can probably correct this, but as a starting point, I think this works out as the sum:
(a=0 to n) Σ(100x1.05ª)

From here: moneychimp.com/art…htm

So I think you'd have:
c[ ((1 + r)^(Y + 1) - (1 + r)) / r ]

where c is your investment (100), r is your interest rate (5), and Y is your length of time (50)?

I haven't tried it out so I'm not sure this is what you're after... the link gives extra detail if you have an initial sum at the beginning of the period...