Help With Compound Interest Calculation

Rockingsurfer

I need to accumulate £4000 in my soon to be opened mini cash ISA in six years. I also have intermediate savings aims and need to remove the following amounts from the account at the end of the following years

Year one £500
Year two £1000
Year three £1800
Year four £1500
Year five £1200

You will notice that the total amount to be saved is £10,000 and that I have 72 months to achieve that total. This means that ignoring interest earned I must save £138.89 per month and that since the largest part of the amount required is needed at the end of year six it is possible to do this with a monthly savings amount that does not need to change over the period.

In fact the ISA will be paying 6% interest, for the purposes of this post I have assumed that this rate will not vary over the period, I know this is unlikely but we have to assume something! Can one of you very clever people tell me how much I actually will need to invest per month to achieve my aim as it obviously is not £138.89 as I have six years of compound interst working in my favour. Even better can you tell me how to work out the maths for myself so if these figures above (which are provisional) change I can work it out for myself rather than bothering you all again.

If it was as simple as working out the amount required per month to save 4K in 6 years with a compound interest rate of 6% pa I could do the maths myself but I cannot handle the complictions caused by the intermediate amounts.

TIA
RS

MrChips

You need to sum the following terms to determine the lump sum you would need to invest now to meet your aims above:

500v + 100v^2 + 1800v^3 + 1500v^4 + 1200v^5 + 4000v^6, where v = 1/(1+i) where i is the net rate of interest after tax, 6% in your case (although this isn't guaranteed to last forever).

with i=6%, you need £7,777.70 invested right now. However you wouldn't be allowed to put this into a mini cash isa in one lump sum, and you express a preference for regular savings anyway.

Therefore you need to equate this lump sum with a regular stream (say monthly) of contributions.

Again with i=6.0% you get this equation:

fixed monthly contribution needed at the start of each month = 7777.70 * (1 - 1/[(1+i)^(1/12)]) / (1 - v^6) = 127.69 when i=6.0%. You can vary the interest rate to come up with different lump sum and monthly contriution options, and the "12" in the final equation can be varied to alter the number of contributions per year.

Rockingsurfer

:beer:

Dear MrChips

Thank you very much for your help. I thought I was being thick when I couldn't do the sums. Having seen your solution I now know I could never arrived at the answer for myself.

I'm sure many people have a long term savings aim with intermediate smaller aims, it is a pity this fromula will disapear from the front few pages of the board within a day or two.

Thanks
RS