Regular saving v fixed rate accounts

Redress wrote:

Is there a method of working out the best return. Ideally I would like to develop an excel file to work this out where the variables are the interest rates.

Regular saving account:
y - AER (for example, AER=7% y=0.07)
s - monthly amount

m - monthly interest: m=(1+y)^(1/12)-1
k=1+m

Resulting amount after 'n' months: Sn=s*k*(k^n-1)/(k-1)
Resulting amount after 12 months: S12=s*k*(k^12-1)/(k-1)=s*k*y/m
I - total interest earned after 12 months: I=S12-s*12=s*[k*(k^12-1)/(k-1)-12];

Approximately 'I' can be estimated as Ia=6.5*s*y. The error when using this formula is less than 1.5% for y<10%.

‘Drip-feed’:
If you have lump sum s*12 and use some instant access saving account to ‘drip-feed’ regular saving account you put ‘s’ into regular saver and 11*s into saving account at start. For 12 months saving account will earn (hereafter ‘y’ and ‘k’ are for saving account):
I=s*12*(1+y)-S12=s*12*y- s*k*(k^12-1)/(k-1)=s*(12*(1+y)- k*(k^12-1)/(k-1))
Ia=s*12*y-6.5*s*y=5.5*s*y

Good luck :wave:

bernardh wrote:

What a saddo. Probably reads the `Penguin Dictionary of Curious and Interesting Numbers` for fun.
Just like me.
The kids think I should get out more.

I referred to my copy earlier today - to try and answer Martin's Money Poser!