Compound Interest calculations

meester

Graeme7777 wrote: »

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!

Loan interest is often calculated monthly. This benefits the bank, because your repayments do not get taken into account immediately.

For savings they do it daily, otherwise you could put money in on the last day before interest is calculated and earn extra interest.

CLAPTON

meester wrote: »

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

actually the one bit I agreed with is that interest is charged daily... its other other bits I dont agree with.

basically you can't work out the daily rate from the APR without knowing how the compounding works and it you want a formula that is general then it must work for small amounts of time as well as long period of time .. hence my example.

hollymcr

Phew! As the OP I have to say I'm impressed by the response (and very grateful for the replies).

My maths degree was actually mathematical physics so didn't really go into this stuff, but I do know (or have recalled in reading this thread) enough to understand most of the replies.

I'd reached the conclusion myself that it would require numerical methods to solve this, but I had no idea Excel could do this, so that's something to look for (I don't use Excel much). It's nice to know my gut instinct was right that there isn't a simple solution, though.

As to whether T1/T2 are days or years, whether interest is paid daily, etc - to be honest I'd be happy with whatever assumptions people made, as this has become more theoretical than practise. I was working with complete years to make things easier (if still unsolvable!)

To push my luck a bit, if anyone can tell me how to solve something like this numerically in Excel (I had a quick Google but didn't find any good answers) I'm sure my Dad would be even more impressed. Regardless, though, thanks to everyone for the interesting thread.