Compound Interest - AER vs Gross - is it right?

KianM

I was reading the "Interest Rates Guide" (can't post a link - it's [MSE]/banking/interest-rates) and it said that gross rate is what is actually paid and AER is the effective interest rate if it was compounded yearly. That's what I thought but then the example given confused me:
"For an identical account, if interest was paid monthly it would be a 4.89% gross rate, but if interest was paid annually it would be 5% gross. Leave the money there over a year, though, and both would receive the same amount, as the AER for both is 5%."

If it's paid and compounded monthly, surely the rate would be (1.0489)^12 = 1.773... i.e. 77.3% yearly?

This is the same with HSBC's rates (AER 2%, 1.98% gross, compounded monthly - gives 26.5%) which is why I think I'm missing something?

jimjames

No it wouldn't.

The rate isn't 5% per month. It's 5% per year.

The monthly amount is 5/12

KianM

Ahh! Thank you! So gross rate is like the sum of all the monthly gross rates - fairly useless though. It seems like a rather odd way of presenting it but it does mean you have less work to do in calculating the monthly amount.

So instead it's 4.89/12 = 0.4075%/month, (1.004075)^12 = 1.0500 => 5%

jimjames

KianM wrote: »

Ahh! Thank you! So gross rate is like the sum of all the monthly gross rates - fairly useless though. It seems like a rather odd way of presenting it but it does mean you have less work to do in calculating the monthly amount.

So instead it's 4.89/12 = 0.4075%/month, (1.004075)^12 = 1.0500 => 5%

Yes, I'm afraid so.

It would have been nice to get 77% on savings though!

KianM

Haha yeah! You'd add an extra 0 onto your balance about every 4 years!

eskbanker

KianM wrote: »

So gross rate is like the sum of all the monthly gross rates - fairly useless though. It seems like a rather odd way of presenting it but it does mean you have less work to do in calculating the monthly amount.

Gross rate is particularly relevant in the context of all the accounts where interest is only paid on a capped amount and therefore if you max out these accounts there is no compounding possible in order to achieve the AER.

In other words, if you have £2K in a TSB 5% AER account (where no interest is payable above £2K), then the maximum interest you can earn is 4.89% (less tax).

KianM

Good point, thanks!