Compound Interest calculations

MRLX69

Toastie wrote: »

S = S1 (1 + r) n

S = The future value of the amount invested
S1 = Original amount invested
r = rate of interest, expressed as a proportion(i.e. 4% = 0.04)
n = the number of year for the investment.(I.e 6months = 0.5)

This is how you work out compound interest, but i was never good at re-arranging algerbra

There're two lump sums invested at different times, that's the main problem. If everything was invested at one time, then it would be what you've said.

sloughflint

meester wrote: »

I think it is reasonable and appropriate to assume that interest is calculated daily (whether it is PAID daily, monthly, or yearly, makes no difference at all), or otherwise that t1 or t2 are integer numbers of years.

I hadn't put much thought into it when I posted and still haven't but my gut feeling was that if an interest payment had been made within the timeframe, this would need to be factored in and complicate things a bit more.

sloughflint

I can tell that I'm going to start playing around now. Not good news at this time of night. Lol

meester

CLAPTON wrote: »

the OP says he is a maths graduate, so no I don't think it reasonable to make such assumptions

but it's not a maths graduate problem, it is a real world situation.

Find me a bank account that DOESN'T calculate interest daily.

Do let me know

meester

sloughflint wrote: »

I hadn't put much thought into it when I posted and still haven't but my gut feeling was that if an interest payment had been made within the timeframe, this would need to be factored in and complicate things a bit more.

It doesn't make any difference.

If you invest £100 on January 1, and the AER is 10%, then on January 1 next year you will have £110 - it makes zero difference whether all the interest is credited at the end of the year, daily or monthly, because it's an annual EQUIVALENT rate.

If you add £150 on July 1, assuming interest is credited monthly, AER is 10%, and the account is closed after two years, then you have

£100 * 1.1 * 1.1
+ £150 * 1.1 * (1.1)^6/12

Whether any of the interest has been credited yet or not cannot affect that if the AER is 10%, then your initial £100 MUST be worth £110 after 1 year. Of course any money will added will earn interest as well, and after that has been there 1 year, it will have grown by 10% as well.

sloughflint

Yep, thought about it now. Phew, can go to sleep now.

Toastie

MRLX69 wrote: »

There're two lump sums invested at different times, that's the main problem. If everything was invested at one time, then it would be what you've said.

Would you be able to double up the S1 (1 + r) n part by adding S2 (1 + r) n
N would be in months then rather than a year.

E.g S1 (1 + r) n + S2 (1+r) n

meester

Toastie wrote: »

Would you be able to double up the S1 (1 + r) n part by adding S2 (1 + r) n
N would be in months then rather than a year.

E.g S1 (1 + r) n + S2 (1+r) n

it is (1+r)^t1

Which doesn't distribute with the other in t2

Meltdown_2

What doesn't seem to have been spelt out is that the AER is a "notional" rate.

Its purpose is to enable potential customers to make a 'real world' comparison of accounts across the marketplace. It relies (in making an assessment of it) on a number of assumptions. These will vary according to the account under consideration - a notable complication in recent years has been the introduction of short-term 'bonuses'.

Graeme7777

Hi,

Can one of the maths boffins please explain the difference between interest being calculated and paid? With a "normal" loan that one repays monthly, is interest calculated daily or monthly?

In the formula used to calculate the monthly payment, should one divide the annual rate of interest by 12 or 365?

Thanks!